# JPRS ID: 10326 TRANSLATION PROCEDDINGS OF THE FOURTH ALL-UNION SYMPOSIUM ON CONTROL PROBLEMS IN COMMUNICATIONS NETWORKS AND CENTERS ED. BY V.G. LAZAREV

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i~()R nF'FI('IA1, IItiF: ()NI,Y
JPRS L/ 10326
16 February 1982
~1S~CItIQI~
Tra
~~QCEFDINGS OF THE FOURTH ALL-UNION SYMPOSIUM
~JN CONTROL PROBLEMS
IN COMMUNICATIONS NETWORKS AND CENTERS
~d. by
V.G. ~azarev
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JPRS L/10326
16 February 1982
PROCEEDINGS OF THE FOURTH ALL-UNION SYMPOSIUM
= ON CONTROL PROBLFMS IN COMMUNICATIONS NETWORKS APJD CENTERS
- Moscow TRUDY IV VSESOYUZNOGO SIMPOZIUMA PO PROBLEMAM UPRAVLENIYA NA
SETYAKH I UZLAKH SVYAZI in Russian 1981 (signed to press 26 Feb 81) .
pp 1-156
jBook published under the auspices of the USSR Academy of Scierrces,
Information Transmission Problems Institute, edited by Doctor of Tech-
nical Sciences, Professor V.G. Lazarev, Nauka, 350 copies]
CONTENTS
Annotation 1
Problem of Dete rmining the Load on Centralized Control Units at
Switching Cenrers. R. A. Avakov, V. D. Safronov 2
Estimating the Operating Efficiency of the Control Complex of a
Switching Center. E. Kh. Allayev, M. Sh. Zakhitsov, A. S. Saibov 5
, Influence of the Traffic Control Algorithm on the Transmission
Characteristics of Multipacket Communications. A. V. Andrianov 9
Estimating the Efficiency of a Model oE the Game Method of DynamicControl of a
Communicat-ions Nc~twork. P. V. Bershteyn, P. I. Kozhemyakin 12
Estimating the Reliability of Commimication Netwarks with Nonideal
Control. V. A. Bogatyrev, Yu. M. Martynov 15
Analysis and Sh ort-Term Forecasting of Telephone Traffic.
R. P. BoriGova, T. D. 7.elentsova, A. P. Pshenichnikov 19
Real Time Dispatcher for a Pro~;ra~ned Subscriber's Station.
Yu. P. Gal', V. I. Colovach, V. M. Sobol', Ye. G. Stalin z2
Analytical and Statistical Simulation of the Telephone Operation System
of an Electronic Switching Center. B. S. Gol'dshteyn 25
Methods of Dynamic Dispatching of Problems in Computer Networks.
K. R. Guaryan, V. M. Konovalov 29
- a - [I - USSR - F F(?li0]
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~teth~~ls ot iusuriub ~~~>~ratin~; titahi.lity ~~t a P1~55a~;e 5wit~~hiiiY, Ne~w~~~'k� 33
I. M. Gurevicti, V. K. Demin, V. M. Chentsov, Ya. Shorgin
Method of Improving the Service Quality on a Channel Switching Network
with Dynamic Control. A. Y a. Dolgoselets, N. A. Knyazeva, L. A. Nikityuk 38
Overload Protection in Channel-Swicched Networks, V. M. Dubrovinsk~y 42
Problem of Channel Distrib ution in the Digital Data Transmission Network ~6
for Railroad Transportation. Zh. Dusembayeva
Switching Control in Railroad Transnortation Long Distance Telephone 48
- Service. S. L. Dyufur, Yu. V. Yurkin
Control Algorithms and CarryinK Capacity of Switchin~ Systems. 51
V. A. Yershov
Problems of Designfn~ Developed Networks of Collective-U3e Compu.*.er 55
Centers in the Dialog Mode. Yu. P. Zaychenko
An Approach to Optimizing the Structure of. a Large-Scale Data T.rans- 60
mission Network, G. P. Zakharov, V. V. Lokhmotko
Time Decomposition of an Automaton: L. N. Zoreva, V. G. Lazarev 65
, Distributed Control in Switching Centers Using Microprocessors. 67
0. N. Tvanova
- Software for Supplement~y Services of the 'Kvant' Quasielectronic 71
Automatic Telephone Office. A.A. Iv.anov
- Choice of Dynamic Control Method for Information Flows on a Communications 76
Network. Yu. M. Kazachenko
Selecting Types of Processors for a Multiprocessor System. ~
A. N. Kol'tsov, F. I. Pepinov
Homeostatic Principle of Regulating the Outgoing Subscriber Traffic.
- A. V. Kotov 83
Research of the International '~elephone and Telegraph Consultative
Committee in tlie Field of Ner~iork Control. A. V. Kotov 88
Some Characteristics of Packet-Switched Data Transmission Systems.
V. N. Kosilelev 9~'
Simulation ~f Programmed Control Processes in Switching Centers.
Ye~. V. Konovalov 9~
- Consideration of the Length of Transmitted Messages for Routings in
Channel-Switched Networks. N. I: Kuznetsov, 0. N. Romanov 101
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Influence of Control Function Distribution on Output Capacity of a
Multiprocessor Control C~mputer. S. Sh. Kutbitdinov 105
Routin; Algorithms and Communications Quality in a Multipolar Data
Transmission Network. N. P. Krutyakova 108
Structur~l Principles of an Automated Design System for Inrormation
Distribution Systems and Devices. V. G. Lazarev, N. Ya. Parshenkov,
Ye. I. Piyl' 112
Introduction of a Method of Setting Up Calls With Alternative Routings on
Rural Telephone Netwo rks. Yu. Lazarev, S. A. Krasnov 115
Influence of the Carry ing Capacity of Switching Centers on Dynamic Control
Efficiency. Yu. V. Lazarev, I. V. Nikiforc~va 118
Application of the Methods of Dynamics of Means for Estimating the
Efficiency of I)yc~amic Traffic Control in Networks with Queues. Yu. A. Lev 121
Call Distribution Algorithm on Prospective Rural Telephone Networks.
- I. 0. Litsit 124
Some Results of Comparing Two Methods of Calculating Losses in
Communications Networks. A. I. Movshovich 128
Set of Programs for Calculating Losses in Communications Networks by
the Combined Method. A. I. Movshovich, M. Yu, Khokh7~va 132
Application of Special ized Processors in tl~e Control Units of Switching
Centers. A. G. Popova 138
Systems Approach to Control Systems at the Junct'ions with Different
hlethods of Delivering I~essages to the Networks. V. N. Roginskiy 141
Dynamic Contrul of Brancn Capacities in a Channel Switching Network.
; 0. F. Sergeyeva 143
Mathematical Model and Hstimating the EEficiency of a Message Delivery
Contr.ol Technique Based on Joint lpplication of External and Internal
Priorities. V. N. S il.ayev, Yu. F. Zolotykh, L. M. Bondar' 146
- Study of Methods of. U r~.inizin~ Call Servicin~ in the Control Computer of
Com~~uter.ize~l Swilcliin}; CenCer. A. V. Solov'yev 150
Se~me Methuds of Impruvin~; the Carryin~; Capacity of. a Cnannel Switching
Netwc>rk. C. L. Slepova 153
Redistributiun of Problems in a Microprocessor Control Network with
Failures. Ye. N. Turuta 157
Man-Machine Method of Obtaining an Algorithm for the Operation of a
Control Unit. L. K. Yan's}~ina 162
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A Vti OTAT I Oti
~ [Text] The given collection includes expanded summ2ries of the reports presented
at the Fourth All-Union Symposium on the control oroblems of communications
networks, the constructian of dynamic information flow control systems, the prob-
lems of introducing control systems in the communication; networks and centers of
the USSR and the construction of Pro~rammed control devices. In addition, a
study is made of the analytical methods of analyzing networks with dynamic
traffic r.ontrol and the problems of their application in practice.
1
~
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r~rn vrr~. u�.. �,..r.
PROBLErf OF DETERMINZNG THE LOAD ON CENTRALIZED CONTROL UNITS AT SWITCHING CENTERS
[Article by R. A. Avakov, V. D. Safronov, Leningrad, pp 3-SJ
When developing centralized control units (CCU) based on control comp uters (EUM),
a number of peculiarities arise in determining the incoming and senriced load.
These peculiarities are caused by the multiple staging, the presence of prioritie$
and temporary restrictions in servicing the calls [1-3].
The incoming telephone call traffic creates a load on the switching center (SC).
The load serviced by the switching center with given subscriber servicing quality
nor~s determines the carrying capacity of the switching center as a whole. The
carrying c:apacity of a switching center with programmed control depend~ on the
carrying capacity of the switching system (SS) and the centralized control units
(CCUj. Let us stipulate that the carrying capacity of the CCL' be expressed in
terms of its output capacity, which will be determined by the ~aximum number of
serviced calls per unit time under the condition of the presence of a sufficient
ntm~ber of SS imits. Thus, the output capacity of the CCU can be expressed in
terms of the load for which it has the meaning of efficient application of the
CCU.
The servicing of calls in the swirching center with program control is divided
into a number of stages which are determined by the type of communications, the
typ e of commtimication area, the actions of the calling and called subscribers.
Each stage of servicing the calls corresponds to setting up a call
(discotmectingl in ~he switching system between the incoming and outgoing equip-
~nent (lines).The flow of calls coffing to the switching system "multiplies" on the
basis of multistaging and limitation of the functions of the SS sets, and it
detez~mines the flow of requests to the CCU. The requests to the CCU come fron~
sources which are the various types of SS sets. The prncess of servicing the
requests consists in successive processing of calls in the CCU-SS section [4].
There is a dependence of the load ~YCCU~ coming to thP CC~1 on the load ~YSS~
coming to the SS: YCCU-f ~YSS~' ~ YSS increases, Y~~ also increases; CCU is
considered to have exhausted its output capacity when it cannot service an addi-
tional load without having a negative effect on the subscriber service quality.
Here the difference between the incoming load and the load serviced by the CCU
will determine the service losses of the flaw of requests ~Y [1]. In reference
[5], let us present the possible methods of estimating the carrying capacity of
the SS with programmed control.
2
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6'l)N (?}'F'i(7~~1 l ~b' t)1~L1
From the point o~ viaw oE program processing, aactt stage of servicing is a separate
problem which is realized in the CCL` by means of three processes: information
reception, processing and output. Representing the operation of the CCU in the
form of a single-routing queueing s~stem ~or each of the stages, it is possible to
obtain all the necessary characteristics (waiting time, busy period, and so on)
of each of the processes which are required to estimate the load on the CCU.
~ formalized description of the process of servicing the CCU calls can be
rep resented in the form of a graph:
~ _ {A~B} ,
where A={al, an} is the set of apexes of the graph which correspond to the
call servicing stages; B={bi�} is the set of sides of the graph whi~h reflect the
information interrelations o~ the call servicing stages and are given by che matrix:
'i for i=j ,
B=116,~ y = 6Ld in the presence af a side,
0 in the absence of a side.
FYom the matrix B, which is a mapping of the graph G, the set of routes traveled
by the call servicing stages between apexes ai and a~ i, 7=1,.:,n is determined.
The call servicing route (sequence) is also given by ~he transmission matrix:
P=Mp~,
where pi~ is the probability that after servicing at the apex ai the call will go
to apex a~ for servicing.
Each apex of the graph G forms its own flow of requests to the CCU in accordance
with the load intensitv of the i-th flow (.~i). The flow of requests coming to
the CCU for servicing is characterized by the times of their arrival ti and the
servicing time of the requests in different stages c~Ti. The times ti are deter-
~ mined by the actions of the subscribers (picking up the receiver, beginning to
_ dial the number, and so on). For determining ~ti through a given SS it is
necessary to know the number of operations executed in the i-th sta~e ki (it is
- determined by the logical diagrar~ of the algorithm) and the duration of each
operation ^ti (it corresponds to the time spent on performing an elementary opera-
tion):
,j~~-,;; et~ .
The flow of requests reaching the CCU creates the load:
~
YCCL' = 7 , K: ~t .
.~t
In addition to the basic time tproc-~ ~Ti spent on processing the requests to
the CCU, it is possible to isolate constant time expenditures on the performance
of s~stecas operations tso, the operations of scanning the SS sets tsc n and the
variable time expenditures connected with the maintenance servicing o~ the system,
t~in. ~11 of these components can be related by the coefficients q defining the
proportion of them out of the total operating time T:
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hUK tlrrlllnL u7G ~11~a.~
tg~-q1T~ tscan-42T' tproc+t~n=q3T.
Considering the coeff~cient a, operation of the CCU without overloads is guaran-
teed:
~1`~s;`i~ =dT.
The time expenditures tSO and tS~~ create a cons tant load on the CCU independent
of the number of incoming req uests. When determining t.he load connected with
processing the requests, it is necessary to consider the constant camponent which
takes up a significant proportioa~ of the total load on the CCU.
A study is made of the estimation of the effectiveness of functional organization
of request servicing processes in the CCL' by the load criterion. The optimization
of the call servicing processes is carried out by minimizing the nonproductive
- machine time expen ditures. De termit~ation of Che load permits estimation of the
duration of the CCU and generation of recoma~endations for effective use of the EUM
in the switching centers.
For proper calculation of the switching center control equipment it is necessary
to have systematic statistical data. The formation of the statistical information
on the call service quality in the CCU can be carried out on the basis of the load
calculation programs.
_ BIBLIOGRAPHY
1. Lazarev, V. G. ; Piyl' , Ye. I. ; Turuta, Ye. N. PROGRA~MI~II~IOYE UPRAVLE NIYE NA
UZLAI~I KOI~ICITATSII [Programmed Contro]. at the Switching Centers], Moscow,
Svyaz' , 19 78.
2. Ivanova, 0. N.; Popova, A. G.; Solovoy, Yu. V. UPRAVLYAYUSHCHIYE
USTROYSTVA KVAZIELEKTRONNYKH K0;-4tUTATSIONNYKH SISTE.I [Control Units of Quasi-
electronic Switching Systems], Moscow, Svyaz', 1975.
3. BRAND, J. E.; WERNER, J. S. "Estimating the Output Capacity of a Processor
when Processing Calls in a Switching System with Control by a Given Program,"
TIIER (translat~:d from the English), Vol 65, No 9, 1977.
4. Safronov, V. D.; Chagayev, N. S.; Yurikov, N. K. "Estimating Load Intensity
at the CCU in the Switch ing Centers," VSESOYUZNAYA NAUCHNAYA SESSIYA,
POSVYASHCHEi~1NAYA DNYU RADIO: TEZISY DOKL. [All-Union Scientific Meeting in
Honor of Radio Day: Summaries of Reports], Moscow, 1979.
S. Villar, J. E. "Traffic Calculations in SPS Systems," PROC. 8th INT.
TELETRAFFIC CONGR., Melbourne, Vol 2, 1976.
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ESTIi4ATING THE OPERATING EFFICIENCY OF THE C(iNTR(~L COMPLEX OF A SWITCHING CENTER
[Article by E. Kh. Allayev, M. Sh. Zakhitsov ,:nd A. S. Saibov, Tashkent, pp 5-9]
The control system of the switching center must operate continuously over a pro-
longed period, for failure of the control svstem can lead to interruption of the
operation of the entire system. In order to insure high reliabili ty of the con-
trol system, the two-computer principle of switching center control is used [1].
The two-comp uter control system (DUK) is made up of two identical control computers
(EUM). Depending on the selected operating conditions, either one EUM or both of
the EUM simultaneously can be used to service the incoming call traffic.
The operation of the DUK can be organized in the following modes:
Asynchronous (s=1) ,
Synchronous (s=2) , �
Load separation (s=3) ,
Source separation (s=4) .
In the asynchronous mode of operation of the DUK, the f~ctions connectecl with
servicing the incoming calls are performed by the active EUM (EUM-A), the other
(EUM-B) is in "hot" reserve [2 In the case of failure of an active EUM, the
reserve EUM takes on the functions of controlling the switching center. The
operating fitness of EUI~-A and EUM-B is monitored autonomously using hardware
and software (logical program or test) monitoring means. In contrast to the hard-
ware, the software monitoring is accomplished periodically with a period of Tper~
and it requires expenditures of EUM time equal to Tper. After detection of a
failure in the active EUM, the reserve is put into operation after a time interval
tres '
In the svnchronous mode of operation of the DUK, each incoming eall is processed
in parallel by two EiJrt [3]. The res ults of oneration of ths EUM-A and EUM-B are
compared in order to monitor the fitness of the EU1~! in defined phases of call
processing or periodically (with a period of T~o In the case of noncomparison
of the results of the EL'M-A and the EU1~E-B, each o~ them includes the monitoring
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� 1'VK l?tl'1~ ~~~1 \~.�P
4~r~,br3iu5 E~r,~vL~li~?~ tur T LRCil[l~ the raila~i ~Ul~l. fietore repair of the failed EUI~1,
the fitness of the EUM that is in working order is checked by the hardware and
software.
In the load division mode the incoming ca~l traffic is also serviced in parallel
by the EITI~A and the ELR~f-B [4 However, in contras ~ ~o the synchronous mode,
the EUM-A and the EU:I-B process different calls. Or. failure of one of the EUM,
the entire load is picked up by the other. After elimination of the cause of
failure, the initial structure of the DL'K is restored. In the mode with load sepa-
ration, the fitness of the EiTNE-A and EUI~-B is also checked autonomously using
hardware and softwar~ monitoring means.
~ The mode with division of sources is characterized by the fact that all of the
load sources of the switching center are divided into two groups. The calls
coming from the first group of sources are serviced using the EUM-A, and the calls
f rom the second group of sources, by the ELTN~B. On failure of one EUM, the oth er
(the one in good repair) services calls coffing from all the lnad sources. The
fitness of the EL'I~-A and the ETJI~f-B is checked autonomously using hardware and soft-
ware.
The above-investigated operating conditions of the DL'K are ~ot equivaler~t, for they
provi.de for different output capacity and require different expenditures; for
organization of the interaction of the EUNt. Therefore the problem of de:termining
the operating mode of the DUK in which ma~dm~ output ca~acity will be insured
wi th low expenditures on hardware and software for organization of the interaction
of the EUM is of great interest. For selection of this operating mode of the DUK,
the quantitative characteristic is required which permits comparison of different
versions r~f the DL'K among each other. The output capacity, that is, the number
of calls serviced by the DUK with observation of c~riality indices per unit time,
can be used as this characteristic. Since the calls are serviced by the DUK with
waiting, and the call waiting time characterizes the operating quality of the
sys tem, the output capacity of the DUK can be defined as
~~~,-p~t~td}]~n, cl~
where ~1 is the intensity of the incoming call traffic; P{t>ta} is the probability
th at the call waiting time will e xceed the value of ta; ta is the admissible call
waiting time.
For selection of the optimal operati.ng mode of the DUK using the index (1), it is
first necessary to define the call waiting time distribution functions W(t). The
function W(t) depends on many fact~rs: the arrival intensity /1 and the Gervicin~
in tensity U of the calls, the fai lure intensity A~ and repair intensity urep of
the EUM, the period Tper and the time for performance of the check tests TP , the
period T~o~ and the comparison time T~o~ of the resu].ts of the EUM-A and ~~NI-B,
and the operating mode of the DUK, s.
An efficient operating mode for the DiJK can be selected simply without considering
the nature of the incoming traffic or the time required to service the inc~ming
calls. In this case, i~ ~s e~cpedient to use the use coefficient of the computing
capability of the DL'K n S as the optimalness index of the operating mode ~f the
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DUK. This index is defined 3S the ratio of the total useful operating time of
the EL'M-A and the EUNS-B T~S~ to the total operating time of the two computers 2T
in the operating time interval of the DUK T. that is
cs~ T~5' ~2~
~ 2T ~
The operating time of the DUK T consists of three terms:
_ T= t~'t ~t t 3s (3)
where tl is the time during which both EUM are in proper working order; t2 is the
time during which only one EUM is in proper working order; t3 is the time during
which both EUM have failed.
Let us propose that the probabilities of the state of the DUK Pi~ (i=0.1 and
j=0.1) are known, where i characterizes the state of the EUM-A, and j character-
izes the state of the EiJl~f-B, where 0 is the working state ~f the corresponding
ELfi1, and 1 is the failed state; then
t~�T Poo , t~'T(Po~' Pso), t~�T~ P. ~ (4>
Let us consider the time during which the EUM c~n be busy with servicing incoming
calls as the useful operating time of the DUK T~9~. For de[ermination of the
value of T~S~ it is necessary to calculate the nonproductive expenditures of DUK
time in each mode.
The nonproductive expenditures of DL'K time in the time intervals tl and t2 under
asynchronous conditions are related to the performance of check tests and switch-
ing from one EUM to another. The expenditures of DLTK time on performing the
check tests are (tl/Tper~`pe and (t2/Tper)Tper, and the expenditures connected
with switching amount to 1~.~ ~tl+t2) tres' Where t/T e and t2/T r are the number
of performances of check tests in the correspond~ngpt~me interv~als, and ~~(tl+t2)
is the average number of switchirlgs with the simplest flow of EUM failures.
Therefore the value of T~1~ can be defin.ed as:
,r(') t~-T~T�+ti-Tn'Cp-/~o~t1+ta~~P. ~5)
) (2)
Kev: 1. per; 2. res
I~z the synchronous ~eode the nonproductive expenditures of DUK time are connected
with comparison of the results of the ELT".-A and the EL'M-B (in the time interval
tl) and the performance of check tests (in the time interval t2) . These expendi-
tures are defined as (tl/Tcomp ~Tcomp and (t2/TpeT)Tper, respectively. The non-
pruductive expenditures o: DUK time on performing check tests at the times of
noncomparison of tt-~e results of the ELT~t A and the EUM-B are 2~1pt1'per. Conse-
quently, we have
TCi~=t~-TcT~tt:-~~ T�-2A,{i't,,.
(6)
(i) (Z)
Kev : 1. comp ; 2. p er
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, . . ,
- The nonpradu~tive e`~?~tiditur~~s tn [ti~ lo~d ~nd c+~~~irce dtvi5:c~n mo.l~~:; itre~ r~~l:tt~~~l
only to perEurnklnce ~~t' the clleck t~sts. Here, constdering that in the time int~r-
val tl both E1JM can be busy with servicing calls, we obtain
� t t~ ~7)
~ T~~' ~=2~{t-! ti~~* 1- ,T~ `C~ �
Key : 1. per Tn~~ ~
Considering (2),. (S) and (7), we obtain the expression for deteYmining the use
coefficient of the computing capability of the DUK in various modes: .
W
2 ~ 2(Pao+Po,+P,o)(i-~~I -~�{P~'
j ` 1 ~ T n
2 - z~P��~1- ,Tc -2Ao~n~+~Po~+pio~~i'
a.~~ z ~~P~+ p~ +Po)C~- T~
2 -
Key : 1. per
The discussed comparison method and proposed indices permit sele~tion of the best
operating mode of the DUK and at the same time improve the efficiency of using
EUAi in switching centers.
BIBLIOGRAPHY
l. Lazarev, V. G.; Piyl', Ye. I.; Turuta, Y�. N. PROGRAMrINOYE UPRAVLENIYE NA
UZLAKH KOMMUTATSII jProgram Control in Switching Centers], Moscow, Svyaz' ,
19 78.
2. Sidlo, C. M. A Method for Computer Control Transfer in a Co~nunication
Switching System," ~iERErt 70, Rec. Boston, Mass; New York, Vol 12, 1970.
3. Harr, I. A.; Taylor, F. F.; Ulrich, id. "Organization of the N 1 ESS Central
Processor," THE BELL SYSTEM TEC~ICAL JOURNAL, Vol XLIII, No 5, 1964.
4. Lingelbach, W. "~etaconta L large local exchanges supervision and maintenance
techniques," ELECTRICAL COPQNNICATION, Vol 51, No 1, 1976.
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i~c~x ~~h'r�~c�~:~t t~~N' c~Nt.~
~
INFLUENCE OF TI~ TRA~'FIC CONTROL ALGORITHrI ON THE TRANSMISSION CHARA~TERISTICS
OF MULTIPACKET COMMUNICATIONS
[Article by A. V. Andrianov, Leningrad, pp 9-12]
A study is made of the data transmission ne twork (DT) with packet switching (PS) ,
in which the tratfic is controlled individually for each pair of interacting
subscribers in accordance with the "window" algorithm [1]. The essence of this
traffic control method consists in the Fact that the sender subscriber is for-
bidden to input more than the allvwed number W(the size of the "window") of uncon-
_ firmed packets into the network. Each packet taken out of the network is cor.-
firmed by the receiver subscriber. Therefore the actual maxtmum packet input
rate to ~he network is determined by the rate of removal of packets by the receiver.
Then the analytical method is used to investigate the following characteristics
of the traffic control algorithm: the distribution of the length of the packet
queue at the network output (in the queue before the output subscriber line) and
the effective rate R of data transmission between the two subscribers. The inves-
tigation is performed for the case where %~11 of the packet transmission times
over the subscriber lines and over the ~~ztwork are random variables.
Let a multipacket co~nunication be transmitted between two subscribers connected
to the PS network. The law of arrival of packets from the APinp and also the
process of servicing the packets in the line to the APout are assumed to be
Poisson with intensities of a and u2~ respectively. The packet delay or confirma-
tion time in the network is assumed to be distrib uted with respect to an arbitrary
law with mean values of t~l and tc2, respectively.
The packet transmission process over a logical connection, considering control is
simulated by a thr~~e-phase queueing system.
The first phase a W-line queueing system without a queue simulates the trans-
mission process of data packets of the investigated logical connec:tion over the
ne twork. The equipment b usy time corresponds to the random packet delay time in
the network.
The second phase simulates waiting of the packets in the queue and transmission
over the output subscriber line. The second phase is a single-line queueing sys-
tem with limited queu~~. The third phase simulates the process of transmitting
return cnnfirmations over the network. Its structure is analogous to the struc-
ture of the first phase.
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ruK urr~~~ni. u~r_ ~~iv?.r
The restrictiQn imposed by the trsffic control algorittim consists in ttie fact that
the total number i+j+k of packe ts and confirmations in all three service phases
cannot be greater than W. For equality of i+j+k=W, the input traffic halts.
If we denote the steady probabilities of states Pi�k where there are i, j and k
packets in phases I, II and III, then the system o~ equations relating Pi~k under
the conditions i+j+k1, b ut also in the case of close input and
output rates (p~=1).
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FOR OFFICIAL USF. ~~NLY
Ji N
4tl O `L` ~ d
~
46 ~~~_Q2 6
a
Qy y '~q~t
Z in
QZ
0 Z 4 6 d j 0 I 2 J y~
L
Figure 1 Figure 2
Figure 2 shows the mathematical expectation m of the number of packets j at the
network output and the quantile x0.95 of the distribution P~ as a function of
- u2 (a=1, W=8, t~ 5) .
For illustration of the influence of the oarameter W on the efficiency of the
control algorithm Figure 3 shows the coefficient R=u2(1-P~)/min(a, u2) as a func-
~ tion of the window size for a=1, t~=5 and different u2. The relative effective
- rate R as a function of uZ is shown in Figure 4.
It is obvious that the function R(u2) has an extremal nature. The least value of
R and, consequently, the greatest losses in speed, as the graphs show, are obtained
- for u2=~~P2=1). The minimum value of R~n decreases with an increase in the net-
work delay.
R
=s
J~�ql ~s
QB ~ fc`=/ K f~=1
. Q9 _ ~c _ J
46 QB
qy - 4~ t~=S
Qb'
~
4.f ~ ~ Z f
s
0 Y B /l /6 ti?
Figure 3 Figure 4
~ BIBLIOCRAPHY
1. Puzen, L. ; Zimmerman, U. "Proceedings Handbook," TIIER (translated from the
English), Vol 66, No 11, 1979.
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.
ESTIMATING THE EFFICIENCY OF A~lODEL ~JF THE GAME METHOD OF DYNt1MIC CONTROL OF A
COMMUNICATIONS NETWORK
[Article by P. V. Bershteyn and P. I. Kozhemyakin, Kiev, pp 12-15]
A study is made of a network with channel switching in which the intensity of the
individual items is insignificant by comp arison with the total load serviced by
each b ranch, and therefore the distributed load of the k-th item in practice has
no influence on the losses in the branches and, consequently, on the paths by
which it is serviced.
A comparative estimate of the application of dynamic control in the above-investi-
gated network using a game automaton of the D type [1] and a version of it [2] is
presented in this paper.
Let the flow of the k-th item from some node j be able to be directed over of
the n allowed paths, each of which is characterized by a value of qi (i=1, 2,...,n)
called the probability of arriving, that is, qi=l-pi, where pi is the probability
of failure along the path ui� In this case the prob ability of establishing connec-
tion of the calls of the k-th item will be determined by the value of qk af the
selected path. If the calls are distributed with respect to all possible paths
- using tt~e automaton D, the probability of directing the incoming call to the i-th
_ path will be proportional to qi. Consequently, the probability of getting through
for the calls of the k-th flow using distribuCion by the algorithm of the automa-
ton D will be:
a
n ` ^n~
_ a T ~ ~ ~y Y. Q ~
w ~ *
~ ~ ~ ~ ~ ` r~` q~p (1)
~ ` ~q~ ~13
_
Key : 1. mean
~ A
where: q~p= M1 T .
(1)
Key : 1. mean
The gain by comparison with using one path will be:
_ 2 ~ ~2~
6
BD'~D'~K � ~cp-~k ~ ~
P (lj ~ + Q P'
Key: 1, mean
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I~I1R OFFI('IAI. li~l~: ON1,9'
If ~q is distributed with respect to a law with probability density p=f(~q),
the mathematical expectation of gain
- ~ 9~ o~c 6 t t
aD� f (e4* 4 )~teg,)d(oa)= ~ . (3~
og m.n ~1~ 4`P
Key: 1. mean
_ The percentage of failures (losses) is a normalized parameter. It is known that
such parameters are distributed most frequently with respect to a normal law [3].
Since ~q is a linear function of p, also c1q is distributed by a normal law with
d9.spersion o2q and mathematical expectation Oq=O. In this case the probability
that B>0 can be defined by the formula:
P~~D>~~ =~~5~~~~\ (;,4P~J' ~4~
For estimation of the values obtained, it is possible to assume with acceptable
accuracy for practice that:
~'moz-gmin '{t, ~5~
6g= 6 = 6 .
On a well-operating network h=(2 to 3)'10-2 and qmean-1'10-2; then
2
BD = ~-~~,,,~i = z~5�1~"5 = 0~0025r,G,
P c o~ = o,5sz.
It is interesting that even for q~X q~n=1 and q~an=0.5
BD=5.6% for P(BD>0)=0.566.
It must be noted that when using automata D, almost uniform load distribution with
respect to the allowed pat.hs (qi are almost identical for them) is achieved by
the above-described algor~~thm, although the gain is small.
In order to increase the gain, it is possible to propose an algorithm analogous
- to the one investigated above except that the call is directed to one of the
possible paths with prob~ability proportional to ,~i=qi-a. Here a;q~n is a
constant. In this case
Z (6)
" 6 w
4Dn-~ ~ + .
r? ~i' ~tP -d
~ ~1~ gcP
Key: 1, mean
As is obvious from (6) , qD,~ increases with an increase in a.
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F~c~t~ UF'F'Ic'I:~t t~F' uNt 1
t~or n th~ p~th with a value of qi=q~n does not participate in servicing the
calls o~the k-th item. Successively increasing a, we arrive at the type M
automaton in which the incoming call is directed to the path with the value
qi-qmax' Then
gn~~max~~k.
(7)
The mathemati cal e~ectation of gain wi 11 be
g ~qx
_ gn � f ~g r.~o~c a t) f~g') d~ ~ g n,oac - g, ep .
4r~:n ~8~
- In order to obtain a normal probability distribution law for failures with respect
to different paths with q~ q~n=h, for the above-investigated conditions:
~ 3 = (ito~~5)~,
2
hence
6 ~i � 36 600.
~D � z� ~s
Thus, in channel switching networks with quasisteady probability of losses on
the branches, (that is, not depending in practice on the distrib uted item) the
game method of dynamic control using the algorithm of the automaton M turns out
to be more effective than automaton D.
The gain from using the automaton ~I is proportional to the dispersion range of
the p rob abilities of getting through (qi) alon g the paths, and for the automaton D,
the dispersion of this value. However, with sufficiently high probability (no
less than 0.43) the use of automaton D in the above-investigated form also has
a negative effect on the service quality.
BIBLIOGRAPHY
1. Lazarev, V, G.; Parshenkov, N. Ya. "Game Method of Dyn amic Control of Comnun~.-
cations Network," POSTROYENIYE UPRAVLYAYUSHCHIKH USTROYSTV I
SISTEM [Construction of Control Units and Systems], Moscow, Nauka, 1974.
2. Bershteyn, P. V.; Kozhemyakin, P. I. "Comparison of the Efficiency of
I?ynamic Telephone Network Traffic Control Methods," III VSESOYUZNYY
SIr~OZIUM PO PROBLEtifA~~t UPRAVLE.TIYA NA SETYAI~i I UZLAF~i SVYAZI: TEZISY DOKL.
' [Third All-Union Symposi~nn on Contrul Problems in Commimication Networks and
Cent ers : S uiumaries of Reports Mos cow, Nauka, 19 78. ~
- 3. Gnedenko, B. V.; Belyayev, Yu. K.; Solov'yev, A. D. MATEMATICHESKIYE
~TODY V TEORII N:~DEZI-L~10STI [Mathematical rtethods ~n Reliability Theory],
Moscow, Nauka, 1965.
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ESTIMr1TING THE RELIrYBILI'I'Y OF COMMUNICATIOIVS NETWORKS WITH NONIDEAL CONTROL
[Article by V. A. Bogatyrev, Yu. M. Martynov, Moscow, pp 15-18]
By communications network reliability we mean the probability of the presence of
at least one properly operating allowable path between a given pair of junctions.
_ We shall consider that in a communications network with ideal control all possible
paths between each pair of junctions are pexznissible.
- In networks with nonideal control situations e xtst where there is a path through
the operating ne twork elements, but it cannot be used for information transmission
as a result of absence of information at each co~imications center on the state
of all of the network elements, inaccessibility of individual areas or communica-
tion channels for the given data transmission routing, and so on.
Let us propose that as a result of analyzing a specific control method, all cf the
allowable paths ul~ u~~ un between each of the given pairs of centers can be
enumerated. Each path is given by listing the network elements entering into it:
r~_~,~,~...1}.
The path elements can be co~nunication lines and centers. The probabilit;~ of the
ead.stence of each k-th path element is knc~um and equal to pk. Failures of the
commimication network elements will be considered independent events. The relia-
bility of the i-th path will be
R,=pwP6...pt� (1)
If the given set of permissible information transmission naths consists of inde-
~ pendent paths {us, ut, uZ}, the reliability H of the corresponding informa-
tion routing can be defined by the knawn parallel connection formula
H=4-(~-R~)~~-Rt)... (i-R,)� (2)
In the general case, however, different paths can contain common elements, and
therefore the failures of these paths will be correlated. In reference [1] it
is demonstrated that the formula (2) can also be used in thE general case, but
when the parentheses are removed it is necessary to use the rule
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~ . _
P. p: ~ P~ ~ ( 3)
- The necessity for follor,ring rule (3) forces the calcvlations to be performed
by formula (2) in general (literal) form; here multiplication by each next
binomial doubles the number of tern~s in the general expression for H so that in
the presence of N paths the number of tercr,s in the general formula can reach 2N.
- A method is proposed for signi~icant reduction of the volume of calculations by
formula (2) by using a numrer of simplifying procedures and relations following
from (3). Let us denote the multiplication operation subject to rule (3) by the
ymbol Let us introduce the unreliability index of the i-th element
pi=1-pi. It is easy to see that
P~~ P: ` P;. M~~ P~) P~ f~r ~ P~ ~ P` p~ ~ 0. (4)
Analogously, it is easy to check the correctness of the following expressions:
(5)
P`"P~=P~.
1~ QOQ6' PaP 6~ QQ~�
For illustration of the sequence of the calculations by the proposed method let
us consider a simple commimication network consisting of eight elements:
a, b, c, d, e, f, g, h. Let the control algorithm permit use of only the follow-
ing p aths, the number of elements in which will not exc.eed three
~t~LQ,gJ'~l~lC'd1~rj=+e'~~~~~aLa'7'dJ'J S= `Q,h�d~�
We shall perform the calculation with respe ct to the probability Q of unconnected-
ness of the net~~ork Q=1-H by the recurrent fo nnula following from (2):
(6)
ak"~ti-t ~C~-R~)~Qt-1~Rt~4~-~:0~=4.
Inasmuch as the first three paths in the investigated example are independent
(and in the general case the independent paths must first be isolated and put in
the first places in the list of paths), fur Q3 according to (2), we have (in
order to abbreviate the notatiun we shall arbitrarily stipulate that pa=a,
1-pa a, 1=papb=ab, and so on)
Q~.a6cde~.
Now let us define Q4 using expression (6):
. Qy� Qj_a9d, *(a6 cd e~ Qj-ac~d b c e'~ .
According to rule (3) the repeated e?ements are dropped when the paren~heses
are removed.
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~ Fl1R OF'F'1~7A1. l itiH' ON1.1
s
analoguu5ly, Eor QS we ubtain
QS~Q~-e~i,d~Qy=d8cc~e~-[LQdBc` e~-eF~d(nBcj -a96o,~).
_ In the example of the expression for QS it is possible to f~rmulate the following
general algorithm for calculating the p robabflity of disconnectedness of the net-
work by the proposed method. First, the prob ability of the absence of all indepen-
~ dent paths is described by the parallel connection formula, then the probability
of the existence of the next p ath in the list is ~aritten with a minus sign multi-
- plied by the preceding notation in which only the probability of the existence
of all elements entering into the last path are omitted; then the nrobability of
the existence of the next path is written with the minus sign multiplied by the
- entire previously obtained expression in which the elements entering into the
= last path are omitted, a.zd so on.
- Let a sixth path of four elements u6={a, g, h, f} also be pe rmissible in addition
to the listed ones.
Using the present~~d algorithm and the expression for Q$, we obtain the following
formula for calculating the network reliability with six allowed paths
~ Q6=Qs'a9~~Cgcde -dgce).
When calculating the e.~cpression for Q6 we used the fact that fXf=O. The cofactor
in parentheses, according to (S) permits further simplification
6cae- dgce = ge (cd-dc)= ge d.
Thus, for Q6 we finally have:
p6=a6 cd e~- agd gce e~,dc ~(ag -ag B)-8edag
Let us note that when calculating by the generally accepted procedure the
expression for Q6 would contain 26=64 ter~.
For demonstration of the possibilities of the proposed procedure let us calculate
the increment ~H of the reliability which takes place if we permit the use of
another path u~={e, h, g, b}.
Comparing R~=ehgb term by term with the expression for Q6, we obtain the addition
~ rrom the first term equal to ehgbacdf, and the addition from the third terra equal
to eh gbdcfa; the remaining addition terms are not given according to rule (4).
Thus, the desired increment will be
eH.~-e~6(`ac-3;-dcsa)=e~,96a~ d.
Thus, if the reliabi~ity of each element is 0.9, then the increment will be
0.94(1-0.9)3=6.5�10 .
~ 17
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. .
Estimate~ uE tliis type can be uyeful when determining the expediency of compli-
cating the co~imicatiun network control algorithms accompanied by expansion of
the subset of allowable information transmission paths. For estimation of the
reliability of real communications networks, the dis eussed method was prograIIaned
on a comguter; the entire Iogical part of the calculations are performed using
_ the b uilt-in boolean fim ctions on the rows of bits position-wise representing
elements of the co~unications n~twork. The calculation of the reliability of a
two-pole network with three allowable infor~ation transmission paths on the
YeS-1020 computer takes several minutes of machine time.
- BIBLIOGRAPHY
1. Davydov, G. B.; Roginskiy, V. N.; Tolchan, A. Ya. SETI ELEKTROSVYAZI
[Electrocommunications Networks Moscow, Svyaz' , 1977.
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ANALYSIS AND SHORT-TERM FORECASTING OF TELEPHONE TRAFFIC
- [Article by R. P. Borisova, T. D. Zelentsova and A. P. Pshenichnikov, Moscow,
PP 18-21 ]
For the dynamic design of city telephone exchanges (GTS) one of the labor-
intensive problems is predicting the telephone traffic for newly built automatic
telephone offices (ATS) and predicting the traffic variation on all the existing
coumunication lines as a result of a ch ange in capacity and structure of the
network. Forecasting is realized on the basis of observing the traffic on the
existing network and it consists in developing quality characteristics (descrip-
tion of the observed and expected development trends) and quantitative (point or
interval) estimates.
The traffic intensity is a random variable, but in addition to the random fluc-
tuatians there are stable trends in tfie variation of the average values of the
load intensity with development of th e network. The average load intensity from
one group of sources to another does not remain canstant with development of the
network even if the capacities of these groups do not change. Traffic redistribu-
tion occurs, but, as observations shvw, this process has high ifiertia. The inertia
can be explained obviously by, the effect of a large number of factors having
opposite influence on the investigated process. Under these conditions, from
the large n umber of existing forecasting methods [1, 2], it appears natural to
use statistical methods for predicting telephone traffic load.
The statistical forecasting process consists of. two steps [3). The first step is
analvsis of the data for the observation period and the period of construction of
the statistical model. The construction of the model includes the selection and
substantiation of the form of the equation describing the dynamtcs of the process
(its determined base) and estimation of the parameters of the equation. In the
second step, on the basis of the statisti.cal laws found, the expected value of
the predicted attribute is defined.
The traffic was analyzed for a five-year period beginning in 1970 to 1974 at more
than 100 ATS and 2000 interjimction communication lines of the ~toscow GTS.
Iluring the investigated time period, a Unique seven-digit subscriber numbering
system was used on the network. One, two, Chree and four-million numbering zones
were organized. A study was made of the traffic intensities occurr.ing at the
ATS, the intraoffice, intrajtm ction, on the routings from the ATS to the outgoing
message ,junctions (UIS), from the UIS to the incom:~.~g message junctions (WS),
and trom the WS to the ATS.
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. . . . .
The stability of the increase in capacity of the Moscow GTS on the level of
130,000 ta 140,000 n~vnbers per year, invariability of the macrostructure of the
network during the observation period made it possible to use a very simple
linear relation to describe the deterministic basis for the process and load var-
iaticn in time. The equation parameters were found by the least squares method.
For s,tudyingthe effect of the capacity of indivi dual groups of subscribers on the
traffic flows, the reduced capacities of the ATS were calculated
Nred - Ynu + Ni~Yi~ynu~ .
i
where Nnu is the number of residence telephones for private use; Ni is the
number of sources of the i-th category incl uded in the ATS; yi is the average
intensity of the individual load of the sources of the i-th category; ynu is
average intensity of the specific load of the private residence subscribers.
Let us b riefly en~erate the basic results of analyzing the load on different
communication lines for the investigated observation period.
The intensity of the load occurring on the ATS is Yi. The all-oEfice peak
load hour (PLH) depends on the structural co~osition the ATS sub-
scribers. For ATS with a proporcion of private residence ~elephones in the reducad
capacity uf the ATS, for more than ~0'/, the PLH falls in the evening hours and
and less ~han 40i; in the mornin~. For the majority of the
investigated ATS the ratio of the intpnsity of the load occurring on the ATS in
the PLH to the reduced cap acity of the ATS Y�/N ed i had a trend tow ard insignif-
icant growth. The increase in the specific ~oa~d averaged over all of the ATS of
the first million numbering zone was 0.5'o per year, and the second million zone,
_ 1.2% per year. ,
The intensity of the intrajunction load the total load from the ATS with re-
spect to all ATS of the junction region I, including the ATSi - is YiI. Analysis
of the variation in time of the proportion of the intrajunction load in the load
occurring at the ATS Yii/Yi demonstrated that this ratio had a tendency toward
reduction, and for the l~TS of the first a,illion numbering zone the reduction on
the average was 1.7%, and for the ATS of the second million zone, 0.4% per year.
a relation was discuvered between the proportions of the intrajunction load in
the load occurring a[ the ATS and the specific weight of the capacity of the region
in the total capacity of the network.
The intensity of the intraoffice load of the ATSi is Yii. Analysis of the varia-
tion in time of the proportion of the intraoffice load in the intrajunction luad
Yii~Y'I demonstrated that the magnitude of this ratio increased on the average
by 1.~% per year.
The intensities of the interoffice traffic flows (from ATSi to ATS~ of one junc-
tion region) is Y1~. A deterministic basis was discovered for the statistical
dependence of the ratio of the traffic ir.tensity in the PLH fro m the ATSi to the
ATS� to the intrajunction load of the ATSi on the specific weight of the cap acity
of ~he ATS in the capaci ty of the j imction region I, Y1~ /YiI=f (Nred i~`~red I~ '
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The intensities of the load on the ATSi-UISk lines are Yik (ka1,2,3,4). Analysis
of the dynamics of this load made it possible to trace the process of traffic
redistribution with development of the netzaork. In 5 years the cap acities of the
million n~nbering zones increased as follows: the first million by 1.11 times,
the second million by 1.18 times, the third mi llion by 3.53 times and rhe fourth,
by 3, 42 times. Here the specific weight of the capacity of the first and second
n~%:~ering zones in the total capacity of the network decreased, and the third and
fourth zones, increased. The specific weight of the traffic intensity from the
r~TSi to the UIS-1 and UIS-2 in the occurring load of the ATSi with develop~ent of
the network decreased, and to the UIS-3 and UIS-4, increased. The traffic redis-
trib ution process at the Moscow GTS wa~ also observed earlier, for example, during
the 1953-1963 period [4]. Considering that the developmen~T rredictionnof theaload
million numbering zones do not remain ~onstant in time, p
in the ATS-UIS directions, it is proposed that the dependence of the ratio Yik~Yi
on the specific weight of the ~,apacity of the zone k in the network capacity be
used.
Zntensities of Interjunction Traffic Flows (from UIS to UVS). The study of the
dynamics of these loads for 2000 interjunction routes demonstrated that their mag-
nitude is influenced not only by the capacities of the jtmction regions and net-
work cspacity, but also the uniEorm gravitation factor. Thus, under other equal
conditions, the load intensities to adjacent jim ction regions are greater than
to remote ones.
Load Intensities the WS-ATS Routings. The specific loads incoming from
the WS to the ATS had a tendency towara growthZOne the increase wasrl'105%gper
- and for the ATS o f the firs t million numbering
year, and Tor the second zone, 0.25% per year.
For short-term traffic forecasting in the majority of cases it is justifiable to
assume invariability of the model both i:~ the observation section and in the fore-
casting section. Under this assumption the determination of the e:tpected loads
was realized by estrapolation of the deterministic basis for the obintervals~were.
In order to obtain the interval forec~r, the Eorecasting conridence
calculated. It is necessary to solve the problem of short-term traffic forecast-
ing annually; therefore all of the forecasting calculations are performed by
compute r.
BIBLIO GRr1PHY
1, Yanch, E. PROGNOZIROV~'1NIYE NAUCHNO-TEKhNICHESKOGO PROGRESSA [Forecasting
Scientific and Technical Progress], translated from the English, Moscvw,
Progress , 19 74 .
- 2 Lisichkin, V. A. TEORIYA I PRAKTIKA PROGNOSTIKI [Theory and Practice of
Forecasting], ~Ios caw, Nauka, 1972.
3. Ctietyrkin, Ye. M. STATISTICHESKIYE METODY PROG[~10ZIROVANIYA [Statistic~~l
Forecasting `~ethods), ~toscow, Statistika, 1977.
4. `iaksimov, G. Z. ; Pshenichnikov, A. P. TELEFaNNAYA :VAGRUZIGW `TEST~IYKH SETEY
SVYAZI (Telephone Traffic On Local CormnunicationSNetworks], Moscow, S~yaz',
1969.
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REAL TIME DISPATCHER FOR A PROGRAI~IMED SUBSCRIBER' S STATION
[Article by Yu. F. Gal', V. I. Golovach, V. M. Sobol', Ye. G. Stalin, Moscow,
pp 21-24]
The creation of prospective programmed subscriber's stations (AP) with a wide
spectrum of functional capabilities is connected with the development of software
to control the AP resource~s. The most i~ortant operating, reliability and
cost characteristics of AP depend on the choice of inethods of designing the AP
- software. Let us note that these characteristics have a significant influence on
the efficiency of the corresponding data transmission system as a whole.
A method of developing AP software using the UZOR (real-time operations systems
assignments control) dispatcher is discussed. Brief consideration is given to
the problems connected with implementation of this dispatcher on mini and micro-
computers and the specific nature of its application in A.D.
The AP that we are taiking about is part of co~nmunications systems providing two-
way "terminal-terminal" communications in the interests of remote subscribers.
The activity of remote subscribers is man;fested at the input of the AP as an
integral load. In order not to reduce the operating efficiency of the network,
t?ze r1P reaction must lead the message arrival rate over the co~unication channels.
Consequently, the software-harclware system of the AP must satisfy defined time
restrictions; in other words, the operation of the couununications AP takes plaae
in real time. On the basis of this specific nature, for programming the AP assign-
ments means are required with the use of i~hich the exchange procedures with the
message processing problems or operator activity of the investigated AP are
synchronized. The UZOR dispatcher also permits programming of multifunctional
AP problea~s. The UZOR dispatc!~er is the "frame" of the AP program system, and
the functional components of the software of the investigated AP are based on
this dispatcher.
- The dispatcher controls the following AP resources: the operating time of the
central computer processor; the ready-access memory of the computer; inrerrupts
from peripheral devices ( for example, communication lines , information s torage
and display devices) .
The programs making up the dispatcher correspond to macroinstructions. From the
point of vie~a of the AP software develooer, these macroinstructions expand the
usual set of instructions of the mini or microcomputer making up the AP, permi.tting
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algorithms t~ be wri[ten, individual parts of which are executed in parallel in
real time and asynchronously. These parallel parts of the algorithm are called
processes. The presence of processes is a characteristic feature of the operation
of AP in which several information reception and dispatching problems can be
solved simultaneously.
The number of such parallel-solved problems can vary during operation of the
AP; therefore the dispatcher has means of assigning dynamic processes which appear
for execution of a defined problem and disappear after this problem has been
solved. The possibility of assigning dynamic processes makes it possible to use
the computer memory which is part of the r1P especially efficiently, for on com-
pletion of the dynamic process the memory allocated for solution of the problem
becomes free and can be used to solve other problems.
Not all of the problems solved by the AP have identical importance. For consid-
eration of the relative imuortance of simultaneously solved problems at the time
of appearance (generation) of each process its characteristic, called its priority,
is assigned.
In the computer the processes must have the possibility of becoming synchronized
with one another at certain points in time. In other words, the programmer must
knaw haw to give events occurring in certain processes simultaneously. Usually
at such "meeting points" one of the synchronizing processes ("the sender") trans-
mits the conditional information to the other the receiver"). Each of these
meeting points corresponds to a signal. The nomenclature and number of signals
are selected by the developer of the AP software himself.
Very frequently the expected event consists in the execution of a defined problem.
Synchronization with the event consisting in comple ting the dynamic process can
be realized by using the cooperation operator provided for this purpose. The
cooperation operator is also convenient for "early" curtailment of certain pro-
cesses required, for exa~le, in the case of AP operation.
The processing of interrupts from the peripheral devices of the AP is carried out
using the interrupt waiting macroinstruction. The charact~ristic features of the
interrupt waiting instruction permit a gr~up of like peripheral devices to be
progra~ed (for example, ~everal alphanumeric displays can be serviced by several
processes ex.ecuting the s~lme program segment) .
The L'ZOR dispatcher also includes special devices that simplify checkout of the
A.P software in real time. The programmer can set conditi~ns under which emergency
situations arise disturbances in the operation of the system of implemented
processes fixed by the dispatcher himself and capable of leading to failures in
the operation oF the AP. Th ere is also a possibility of defining reactions to
emergency situations which permits the consequences of the Failures to be recti-
fied.
The follawing charact~ristics of the UZOR dispatcher are noted:
The dispatcher instructions are machine-independent; thus, the dispatcher can be
ex.c~uted on a wide range of computers;
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It is especiall~ efficient to implement a dispatcher based on single-processor
mini and microcomputers with limited readv-access memory size;
The dispatcher is independent of the peripheral devices; the required drivers
(input-output processes) must be prograffined by the AP developer himself.
At the present time the UZOR dispatcher is implemented on the SI~3 minicomputer
and the "Elektronika-60" microcomputer. The total volume of the dispatcher is
less than 2 K of 16-bit words. The software for the specific AP was written
using the MAKRO-II microassembler and the macrolibrary corresponding to the dis-
patcher instructions and operators.
- The experimental operation of the UZOR dispatcher demonstrated the following:
The expenditures of labor on the development and checkout of the software were
reduced sharply;
The AP software developed using the dispatcher satisfies the req uirements of the
given speed of the reaction to events in the external environment (request~ to
receive and transmit data) and res~rictioas on the size of the ready-access
memory used;
The AP software developed using the dispatcher has a clear, fle~dble, simple
structure which permits easy adaptation, accompaniment and modification.
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ANALYTICAL AND STATISTICAL SIMULATION OF THE TELEPHONE OPERATION SYSTEM OF AN
ELECTRONIC SWITCHING CENTER
[Article by B. S. Gol'dshteyn, Leningrad, pp 24-28]
The telephone operation system (TOS) is one of the most important software com-
ponents of the switching center, and it is an ordered set of software organizing
the computing process in real time, that is, at the natural rate of operation of
the switching center ar,d the telephone periphery and providing control of all of
the resources of the control computer (EUM).
The telephone operation system is divided into the nucleus and periphery. The
nucleus of the TOS is the priority queueing system which is the dispatching
mechanism of each specific version of the operation system and is based on a
two-dimensional strategy with absolute-relative priorities. Thus, let N flows of
requests to include N programs e~dst to which N priorities are placed in correspon-
dence. Let these pri~rities be distrib uted in some way with respect to K levels.
On each level k(k=1, 2, ...,K) there are I~ priorities, the requests of which do
not interrupt one another. Thus, it is possible to write a priority inthe form
of a pair of numbers (k, m). On the k level there will be (k, 1), (k, 2)�..,(k, m),
(k, uk) such pairs . Obvious ly, X.
~ ME~N.
In this system the request z(k,m) for a call for calculation of the priority
program (k,m) can be either in the waiting phase /~y/, or in the servicing phase
Z (~E ) ~ ,r~-~-
.J
Then the rule for calling the priority program (k,m) implementing the investigated
strategy with absolurely relative priorities can be described using the follawin~
logical e:cpression:
~ H` 4 v({c~m-l)
m~=~~~,m)a[n n ~c~ti,~~]e[n n ~~~,d~~}t, (i)
~.1 d.t j�~
where
~ H~ ~ for i.0, ~1 S..~t)=1. The e~ficiency criterion
1J i-1 1J
of the jtmction SpD assumes the form
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FOR OF FI('1:1L l ~tiF: ONLI'
t j~~ Y CWd + T:~ ) dt ~
.
~ o js~
where Ti~ is the average time for sendin~ the problem and the results of the
calculations between the i-th and the j-th junctions; W~ is the average problem
processing time on an individual computer. The solution of the differential game
of N SDD is realized both analytically and algorithmically.
The investigated m~odels of decentralized dispatching are used as the basis for
the dynamic load distrib ution algorithms operating in real time [1]. For
estimation and forecasting of the dynamic ch aracteristics of the computers in the
dispatching algorithms, procedures for detexmining the average waiting time in the
queue Wq and average time the problems spend in the SMO (computer) WS operating
under nonsteady conditions are Nplemented. In particular, the procedure for calcula-
tion and prediction of WS is b as~d on the expression
W (t)r WSco~=w~o.
ws~t)'e r if 4Ct) wsci~r,,]'
Prediction of WS for any point in time consisr_s in multiple solution of the above-
presented nonlinear differential equation under various initial conditions for
the junctions in the range of the SDD.
On transition from the Markov mo dels of computers to systems of the M/G/1 type
the basic characteristic of the state of the computer by which the control strat-
egy is formed in the SDD is~ uncoa~ leted operation of U(t) during the calculation
of which the reliability of the user information about the processing time of the
problem in the computer and the actual time for fulfillment of the problem are
considered. For priority queueing (computer)systems U(t) is determined by cal-
culating the busy interval.
Inasmuch as the network computers function, as a rule, under conditions of varia-
tion of intensity of the problem flaws, the efficiency of the SDD(I) depends on
the time ot gathering information about the state of the network reserves. For
~tarkov nature of variation of the load at the computer input, a procedure is pre-
sented for calculating the update period for SI on the state of the computer. The
asynchronous principle of SI exchange, the period of which is selected directlv
in the network junction, is economically most justified.
A comparison of the proposed dispatching methods is made on a specialized
simulation model of the computer net~�~ork. Duting the course of the experiments
i* was es tablished that the SDD(0) and SDD(I) insure reductian of the average
time the problems are in the network bv 1.6 to 5 times by comparison with net-
works where there is no dispatching. The SDD(I) decrease the value of td by com-
parison with the SDD(0) by 9-13% on the average, but they require transmissions
appro:cimately 3 times greater than the volume of SI.
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PI/K ~1FP1~ 1.'\1 l..~~ ~r~\l ~
In urdcr ~u improve thc: ~ifecc ~>t ~iispat~hing, the range of the SUD must be
limited. For SDD(0) the number of available comnuters must not exceed N1=5-6.
A comparative analysis of SDD(0) and SDD(I) with respect to efficiency and complex-
ity of realization demonstrated that the range of application of SDD(0) can be
networks with limited gathering of SI, random load surges and the necessity for
rapid selection of the computer, above all, the network based on mini and micto-
computers. The SDD(I) insure higher quality of dispatching in the presence in
the network of a network metering senrice which is characteristic for networks of
medium and large com~uters.
BIBLIOGRAPHY
1. Vasil'yev, V. V.; Guaryan, K. R.; Konovalov, V. M. "Problem Dispatching
Algorithffi in Computer Network," IV VSESOYUZNAYA SHKOLASEMINAR PO
- VYCHISLITEL'NYri SETYAM: REF. LEKTSII [Fourth All-L?nion Semi.nar on Computer
Networks: Lecture ~bstracts), Part 2, P4oscow, Tashkent, 1979.
2. Bronshteyn, 0. I. "Controlled ;~iultistep Service System," IZV. AN SSSR, 1969.
TEKHNICHESKAYA KIBERNETIKA [News of the USSR Acadecay of Sciences, Techni~al
~ Cybernetics],:1o 2, 1969].
3. Gol'dshteyn, B. S. "Optimal Priority Servicing in EATS Automatic Telephone
Office Software," SISTE?~n iJPRr~,VLENIYA SETYAMZ SVYAZI (Communication Network
Control Systems ~foscow, Nauka, 1980.
4. Boytsova, L. V.; Gol'dshtevn, B. S. "Algorithms for Calculating the Basic
Parameters of a Combined Priority Queueing System," ALGORITMY I PROGR~IMY
[Algorithms and Programs], No 5, 1979.
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METHODS OF INSURING OPERATING STABILITY OF A MESS~4GE SWITCHING NETWORK
[Article by I. M. Gurevich, V. K. Demin, V. M. Chentsov and S. Ya. Shorgin,
Moscow, pp 32-38]
Let G(V,U) be a message switching network; let V be a set of switching centers
of the network (for identification of the network subscribers with the network
centers); let U be the set of network communication lines, ~V~~, ~U~=m;
f1=~~\i�~~ be the matrix of the load presented for servicing where a(ij) is the
intensity of the flow of inessages req uiring transmission from junction i to
junction j; i,jE V and ci~ is the cost of one message of the flow ~(i~).
k
Let V2 be the set of correspondir~g pairs (i, j) , i,j6V and V2=L1 Vi; ViGV2;
(1ViV.~; i#j; i,j=1,2 is the breakdown of V2 into priority clas~es with respect
to ct~st of the messages.
~ We shall characterize the quality of servicing the network subscribers by noru~s
for maximum admissible delays Tki in transmission of inessages of given classes
_ of priurities and the correspond~ng loss norms ~r k of the transmitted messages
where k=1,2. Let us isolate the two causes of lo~ses of inessages: losses of
messages at the network entrance as a result of limiting the load adadtted to
the network and loss of a message (ij) inside the network from limiting the
buffered memory of the network junctions.
Let us propose that the channel capacities of the initial network G and the
message flow distribution rule with respect to G are such that for d(i,j),K
Ti~;Ti~ and message losses are absent.
We shall consider that the message switching network is subject to the effects
of information and sCructural disturbances, assuming that the information dis-
- turbance e(^.) is estimated by the value of ~~ij)EV ~C=1~~~i]*~~lJ~~'100%, where
k
\*i / 11 � is the relative increase in the flow intensity 11~ and ~xk is aweight
coe~fic~ent. The structural disturb ance e(s) is the vector (nl,ml)'100%, where
n1,ml are the relative proportions of failed co~nunication centers and lines of
the network, respectively.
Let:
Ti~ (s ~;,1) Ti~ ~E ) be the magnitude of the delay, the delay norm for the
in~ormation dLSturbance e(:1) for the k-th class of inessages;
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ruK urr~~.~A~ ~~~r_ ~m~,r
Tki (e (s) Tki (t (s) ) be the magr?itude of the delay, the delay norm for the
stYuctursl d~5turbnnce :(s) for tli~ k-th class c~f inessa~es;
~i,(E(A)), irki (E(11)) be the magnitude of the losses, the loss norm for the
in~ormation d~sturbance e(l1) for the k-th class of inessages;
,rki (e (S) nk (e (s) ) be the magnitude of the losses, the loss norm for the
st~uctural di~turbance e(s) for the k-th message class;
(Tk~(e(/1)), Ti3(e(s)), nk~(e(~)), ~i~(e(s)) be some piecewise-constant fimctions;
{9~ be a class of networ~C control procedures.
We shall consider that the cor~unications system is stable with respect to
- information disturbances if for de*(11)?E(~,)?0, where e*(A) is the given
ma:dmum information disturbance, E{9iiC{9} such that
K t
- T :e C~ C")) < T ~e ~~'C~l) ?
_ 7 j~E ( A)~ t 9f L~ ~E. ( A)~ ~
and the system is stable with respect to structural disturbances if for
`~e*(s).e(s)>.0 E{?~}C{5;, where e*(s) is the given maximum structural distur;~ance
such that _
T d ~~~5~~ ~ T ~d ~~~5>>,
n~~ (e >m2 V1.
t(~ ~ ~ m
- 1 1
By the known N1, N2, N~ and B~3 it is also possible to define the number of
channels in group 3.
The investigated procedure permits insurance of almost identical servicing of
each of.the flows coming into the network without introducing structural redundancy.
However, the application of this method encounters difficulties in a number of
cases which are connected with complexity of organizing a supplementary routinp
between the switching offices.
The second method provides for introducing structural redundancy. For calculation
of the addition to the last choice groups the necessary initial data are as
follows:
The admissible magnitude (k) of the increase in total intensity of flows coming
_ into the system with a common last choice group;
The magnitude of the admissible losses (Bg) for the flow itself and the last
_ choice group with an increase in intensity of any other flow.
For the given values, the addition is calculated in two steps:
The losses are determined for the flow itself under conditions of increasing the
intensities of each of the other flows by an amount tor which the total intensity
of the flows coming into the system will increase by k times, and the ~-th flow
is discovered, an increase in the intensity of which causes the greatest losses
for the flow itself;
The addition to the last choice group is determined for which the losses for the
flow itself will not exceed the value of Bg under conditions of increasing the
- intensity of the ;-th flow to the value obtained in step I. In contrast to
procedure I for :.ncreasing the resistancp of the network to overloads which only
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creates identical servicing conditions for a1Z tk~e flows, the second procedure
permits effective protection of each flow. Thus, whereas with a simultaneous
- increase in intensity of several (or all) flaws the total intensity of the flows
coming into the system increases by no more than~ k times, the losses of each of
the flows in the general case will not exceed Bg.
The third metho d of protecting the flow of the last choice group itself provides
for using dynamic flow control means. At the present time many different
methods of dynamic control have been created. One of the methods giving rise to
the greatest practical interest is the modified Granzhan meti~od in which the
threshold x,x. The application of this method permits
efficient protection of the flaw itself. However, when using it;, difficulties
arise connected with selecting the effective value of the threshold taking into
account both the sizes of the groups and the situation developed in the network.
It must be noted that the effectiveness of each of the investigated methods of
increasing the resistance of the network to overloads has still not been finally
established at the present time. This arises primarily from the absence of limits
for the admissible worsening of qtiality of servicing of the flows with overload,
the specific statistics of the inc:rease in flc~w intensity in the networks with
bypasses and also the absence of a technical-economic analysis of inethods.
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PVN VPI'~? ~~.Y~'.
PROBLEM OF CHANNEL DISTRIBUTION IN THE DIGITAL DATA TRANSMISSION NETWORK
FOR RAILROAD TRANSPORTATION
[Article by Zh. Dusembayeva, Alma-Ata, pp 45-47] .
The introduction of automated control systems in railroad transportation has given
rise to the development of the e~d.sting digital data transmission network (PDI).
The number of char~nels of the switched network has been increased, the channel
switching means have been improved, and the volume of automatically transmitted
data has been increased.
A change has also taken place in the network structure, for the flow routings
have changed. New channel switching centers and stations having large informa-
tion exchange with the computer center for which nonswitchable channels are
required have arisen. As a result, the carrying capacity of the switchable net-
work has been enlarged, and the number of stations serviced by this network has
been increased. The information subject to transmtssion over the network is also
clifferentiated with respect to urgency.
Further development of the commtmications network for the automated railroad
transportation control system will take p'_ace by joint use of switchable networks
operating by the method of channel switch:.ng (KK), message switching (KS) and
packet switching (KP) . Under these conditions the most important operating index
- is its reliability which can be placed in correspondence to the probability of
connectedness c+f the graph depicting the investigated network. In the given case
the problem of constructing the optimal network with respect to reliability is
solved by constructing a graph with a given number of apexes and sides in which
the probability of connectedness reaches the maxi.mum value.
When designing a communications network for an automated railroad transportation
control system, another approach is selected: namely, the network structure is
known in general, and it is only necessary to di.stribute the commimication channels
optimally under the condition of satisfying a previously given reliability.
For this purpose let us represent the structure of the communications network as a
fully connected nucleus, the nodes of which are the switching eenters, and the
remaining nodes, which are the subscribers, connected in some way to the nodes of
this nucleus. Here it is possible to state the problem of determining the optimal
ninnber of nodes of the nucleus.
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The probability of a random n-apex graph Gn(t) is defined in reference [1], and
the probability that the random graph G(n,m) is connected is defined in [2].
In reference j3], the network is depicted by the graph Gn with probability of
existence of any side equal to p.
However, in a real network another characteristic is more important: the proba-
bility of the existence of paths betzaeen arbitrarily selected junctions A and B
- which corresponds to the value of P~(Gn). Analogous characteristics (the prob-
ability that the message will get from junction A to junction B) were obt3ined
for the KS network PAg(Gn)�
In the given case a study is made of an information network operating in the KS
and the KP mode, for which the probability that the message will get through P
(n,T) is defined. Then for determination of the initial assigning graph, the
existing network is analyzed, the graritation matrix and quality characteristics
of the function of this network are found. For optimal channel distribution in the
inves[igated network, the assigning graDh corresponding to this network has a
curve which will be called redundant.
On this redundant curve it is possible to select one side each, obtaining the
graph of the corresponding network insuring the same information flows. Consider-
ing the cost index, the longest side of the redundant graph is excluded.
BIBLIOGRAPHY
1. Stepanov, V. Ye. "Combinatorv Algebra and Random Graphss" TEORIYA
VEROYATNOSTEY I YEYE PRIMENENIYE [Probability Theory and Its Application],
Moscow, Nauka, Vol 14, No 3, 1969.
2. Erdesh, P. ; Spencer, J. VEROYATNOSTNYYE METODY KOMBINATORIKI [Probability
Methods of Combinatorial Analysis], Moscow, Mir, 1976.
3. Bogomaz. V. P. "Some Proble~ of Optimizing Information Netzaorks,"
OPTI~QZATSIYA NA GRAFAKH I SETYUCH [Optimization on Graphs and Networks
Novosibirsk, 1978.
47
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FllFi l)F~bIl1Al. l~~N. 111V1.1
SWITCHING CONTROL IN RAILROAD TRANSPORTATION LONG DISTANCE TELEPHONE SERVICE
(Article by S. L. Dyufur, Yu. V. Yurkin, Leningrad, pp 47-49 ]
The railroad transportation long distance service network is separated
from the national network. It encompasses almost the entire territory of the
Soviet Union and corresponds to the railroad network in its configuration. The
necessity for this special network is dictated by the responsible role of rail-
roads as the primary transport system on which high requirements are imposed with
respect to insuring large volumes of freight and passenger hauling and train
traffic safety.
At the present time the development of the network is taking place in the direc-
tion of complete automation of settin~ up ca11s. Accordingly, the problem of salecting
the network structure, the method of controlling the network and optimal value
of the quality indices of the servicing of calls have important significance.
The rai lroad transportation communications network has the following characteris-
tic features as compared to the national long distance co~mmimications network:
The line loads are small and are within the limits of 1 to 15 erlangs;
The ne twork operates with calls on the long distance channels with exp li cit losses
and repeated calling where the probabilit~ of ~aii losses has an a~terage value of
0.2 to 0.3. At the same time the probability of load losses is ci~:~se to zero.
The study of subscriber opinions demonstrates that losses in the peak load hour
of 20% of the calls are considered to correspond to good quali ty of service as
a result of which no significant reduction in the probability of call losses is
planned in the long range forecasting of :~etwork development;
The network has predominantly a single-route structure, but the ne~essity for
increasing its viability has raised the question of broad application of alternati~~e
routings;
The 10-step switching equipment is primarily used on the network; the crossbar
system has been partially introduced. The introduction of c~uasielectronic and
electronic svstem~ is planned in the future.
In the given phase of development of the network it is expedient to use the static
control method. As the calculated loss probabilities with respect to calls are
48
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reduced and modern switchin~ equipment is introduced in the net~aork, conciiti~~iis
will be created for transition to the dynamic method of network control. An
expedient number of bypass routes and the number of branches in each route are
being substantiated. '
On different network levels there are conditions of application of hierarchical
and symmetric methods of constructing the network. The limits of expediency of
each of the methods must be defined considering the costs of the channels, the
incoming loads and the probabilities of losses with respect to calls. Figure 1
shows graphical relations permitting qualitative estimation of the limits of
applicability of the sy~netric and hierarchica~ methods of network construction.
The coefficient F is the ratio of the total cost of the channels of hierarchical
structure to the total cost of channels of a symmetric network. The argument h
- is the cost of one channel of the network branches with respect to the channel
cost in a high-use group for hierarchical structure of the network. Curve 1
characterizes the case where the load coming to each branch of the network is
3 times less than the load coming to the high-use group; curve 3 is the case
where the given loads are as many times greater than the load on the high-use
channel group; curve 2 shows all of the incoming loads identical. For F>1, the
svmmetric structure has the economic advantage.
For a real railroad transportation network, families of configurations were
discovered during the analysis process, and the costs of each version were deter-
mined with respect to consolidated indices Q=K+3'T, where K are the capital expend-
- itures, 3 a~e the operating expenses, T is the return time on investments. In
- Figure 2 as an example we have the relative cost of each version of the network
structure (sy~netric and hierarchical met;?ods) as a function of the ratio of the
branch lengths d. The study confirms the conclusion previously drawn [1] of
expediency of application of the synunetric structure in the majority of cases on
the railroad transportation network.
The intensities of the incoming flows are determined, and by measurements over a
long period of time it was dis covered that a significant increase in them with
respect to the established level has low probability. On the other hand, loads
caused by damage to part of the branch channels or complete failure of the nebaork
branches are possible. Simulation has demonstrated that the symmetric networks
tolerate overloads connected with damage to part of the branch channels better
than the hierarchical network; in the case of total damage to a branch, the network
_ is in practice blocked as a result of an avalanche increase in the repeated cal]s.
In this case the bvpasses must be forbidden.
The pubiished research results provide a basis for assuming that in the case of
small luads and high use of the network channels, control methods with limited
waiting at the call oenerating point and with threshold for tandem loading wi11
have an advantage ~aith respect to the strategy of servicing over direct groups.
49
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. . . _
- ~
(
M, ~uuepapr.
f
/
{02 >S3fte.~2
2
lO.~a~r
_ ;0 J ~o s~
t2)
- 49 p=4Z Q9Q P=QZ
q,f /,0 ~ ~0 1,S ZO T S d
Figure 1 Figure 2
Key:
1� Qs ymm~Qhierarchy
2. erlangs
BIBLIOGRAPHY
1. Dyufur, S. L. "Application of Variable Routing of Calls on a
Long Distance Automatic Railroad Co~nunications Network," AVTOMATIKA,
TELErtEKHANIKA I SVYAZ' [Automation, Telemechanics and Communications
No 3, 19 70 .
SO
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1~OR OFFl('IA1. IIfiH: ONl.l'
_ CONTROL ALGORITHIrISS AND CARRYING CAPACITY OF SWITCHING SYSTEN`,S
[Article by V. A. Yershov, Moscaw, pp 49-53]
Effective estimation of the operating quality of autonatic switching systems
including two fimctionally complex subsystems the control subsystem and switch-
ing subsystem itself is impossible without joint analysis of them and a systems
approach to the given problem. This is manifested especially clearly in prospec-
tive automatic switching systems with control based on a computer where the method
of processing the control information is determined by the call set-up
algorith on which, in turn, depends on the method of finding the connecting paths in
the system.
Let us consider the class of path selection algorithms in an arbitrary multilink
switching sys tem (KS) , which we shall define as follows. Let G~~i~ be a random
(equil'brium) selection algorithm for a free segment of the path in the link i
and Gy~~~ be the ordered selection algorithm for a segment of the path in the
link Then � ~
U~
~'{Gc . Gy ,~E ~1, ~E 7z, 7~ U 1~s~I~ ~ ~1~
where the z-set of links of KS is a path selection algorithm in KS, for which a
random choice is used in the z2-link, and ordered selection of the path se~ments,
in the zl-links.
The most detailed study was made of the influence of the algorithm {G~~i~ ~iEzi
representing the random path selection algorithm in the KS, on the carrying
capacity. The algorithm {Gy~~~IjEz}, which is the ordered selection algorithm,
has been studied appreciably less in theoretical respects. The algorithms of the
more general form defined by (1), were studied only by statistical simulation of
- the operation of the KS on a computer.
Let us consider the calculation of the capacity of a multilink KS when using
algorithms oE the type of (1) . The basis for the approximate mathematical model
is the relations used in the separate loss method (MRP) [1]. According to the ''~P,
the general loss probability with respect to calls p and its components in the KS
operating in the group Einding mode (~I) are determined from the conditions:
PrPg t 1',r, \2)
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Pba ~J-a, c~-N~ e~(~"6 lY~ ~ ,
- Y KL1_E~ 1" ~ e ) c3~
~ 6 1=
P~ Y-d-~ ~L i
P
Pr3~".~ e,r U',r ~ P)' ~4>
K_?c,-!
K~ ~
where pb is the probability of losses with respect to calls as a result of
internal blocking in the KS; Pv is the probability of losses with respect to calls
as a result of all of the outputs of the hunting route being busy; v is the
number of outputs on che hunting route3 Y is the intensity of the serviced
load on the hunticg routing; K1 ~s the number of switchboards of the first KS
link; ub, u~ are the load screening coefficients assumed to be equal to the
following, respectively:
r6 - !'P.r ; (5)
~.,~II ~_p.p,~, (6)
The magnitude of the effective availability d is determined from the expression:
d-(t-x),r;~r2Y, }~(Y-2Y,~ /K 1,
where ~ is the probability of blocking of the routing output; Y1 is the load
intensity serviced by one switchboard of the first link KS; r1 is the proportion of
the serviced load of the first link switchboard routed on the investigated
routing.
For solution of the system of equations (2)-(7), it is necessary to know the load Y
serviced bv a group of v lines, the structural parameters of the KS, the interlin':
cross-~onnection law given by the graph of the paths between the entrance and exit
and the probability n. The value of n depends on the above-indicated parameters
and also the algorithm for selecting the path seg~nent in each link.
Let us find the probability T. For this purpose let us consider how the load on
the KS links is distributed during random and ordered hunting. Let us introduce the
following notation. Let Yr be the load caused by one switchboard of the link r;
y(r,2)(r+l,t) be the load serviced by one line connecting the switchboard 2 of
link r to the switchboard t of link r+l, where r=1,z-1, k=1,kr, t=1,mr. During
random nunting in the link r we shall consider that
'~(2~~)(ti* i,t) =Yi ~mz � (8)
For ordered hnntin~ in link r, beginning with line s, the distribution y(r,?.)
(r+l,t) will be given as follows. If ,
A2=YZ/(t-E~z CAz)), c9)
then
52
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`1~z,c)(t+t,t) =~z~Et-i (~Z)' ~'t ~A:)], (10)
whe re
~+1,..., , ~l, ~-i , if ~ ~ # 4
l,..., ?rit. if ~=1 ~
Let W(r, 2) (rl-1, t) be the probability that the side R(r, k) (r+l, t) of the graph
_ of the paths between the entrance and exit of. the system is busy. Then, if we
as s ume th at
'~~z.c~(z.~,t~ � ~(z,e)Cz+r,t) ~
then the probability graph obtained in this case determines the probability n
for the adopted path selection algorithm.
The problem changes insignificantly if KS onerates in the GI mode with several
attempts to set up a call. In this case, only the expression. for the
probability pb changes. It is possible to show that for v attempts to set
up a call the probability of blocking will be:
m~ ,
~~d.r ~ 1 ~~m:'d~)-d;~]
P6 M1 ~ ,,ti, n "
~d~ ~ 1-~ [z] r i=~ A K~
x� ~(M1,-!).! ' (12 )
E P
i ~~6 ~~l
~ ,
- JYR~ Kt-~ )
_ E~(?n7-d~-!)~~''b t-p K~
where YZ is the load causecl by a group of nZ lines; nZ, m are the number of inputs
and outputs of the switchboard of the link z; d~ is the e~fective availability of
the KS for efforts to set up a call; [x]Z is the probability that vnZ
lines wi11 be busy simultaneouslv in v switchboards of the link 2.
Let us illustrate the proposed method of calculating losses in the KS in the
e:cample of a three-link KS operating in the GI mode with c~rdered path finding
algorithm. The investigated KS has the follc~wing structural parameters:
n1=m1=n 3=m3=k2=h=18, n2=m2=k1=k3 =20, n=1/18. For the ordered algorithm the
p robability of blocking the output of the KS will ba defined by the graph, the
probabilities of a bu5v on the sides of which are found from (9) to (11).
Considering the configuration of the graph (see the figure) for the probability ~r
we h ave :
Tt
~=n ti-c~-w ~1,~>c2.~>>ct-w~~,~~c~,~>>~ . c13>
w~i
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ruK ~hr~~.~w~. UJC. U[VLY
The result5 of theoretical calculatiuns of the luss prubability with respect [o
MRP (equat.ions (2)-(7), (12))and the resuits of statistical simulation for the
ordered huncing algorithm and all links of the KS are presented in the table.
The results of the statistical simulation are taken from [2].
(1,11
Y/V a
_r Pupn__r PuoA
O.o03 O,OIIS O.OI20 + 0,0024 (;W~
0,702 0,0~0 0,0368 + 0,0038 (1 f1 (.1l~-
Q~735 0,064I , O,OG42 + 0,0074 ~
0,762 0,092? 0,0824.0,0066 (2,m~)
0~ 7t3b O~ I289 O~ I I 34 ~ 0, 00'79
Key:
a. MRP
b . MOD
Comparing theoretical data with the statistical simulation data, it is possible
to note good agreement of them. Some overestimation of the data obtained by the
method of separate losses can be explained by the fact that durir~g the calculation
the fact that the calculated loads are of a smoothed nature fail~~ tu betaken into
account [1]. Good agreement of the theoratical data and the statistical simula-
tion data is also obtained in cases where the number of efforts to establish a
connection is limited to the value of v.
BIBLIOGRAPHY
1. Yershov, V. A. KOr~iliTATSIYA NA IVTE~RAL'NOY TSIFROVOY SETI SVYAZI
[Switching in an Integrated Digital Communications Ne twork], Moscow, Svyaz',
19 78.
2. Rahman IQlan, M. M. "Call Packing in a 3-Stage Clos Network," Thesis for the
degree of doctor of philosophy, L'niv. of Strathclyde, Glas gow, 1975.
5 ~F
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PROBLEMS OF DESIGNING DEVELOP~ED NETWORKS OF COLLECTIVE-USE COr~UTER CENTERS
IN THE DIALOG MODE
[Article by Yu. P. Zaychenko, Kiev, pp 53-57]
Among the problems of designing netwarks of VTsKP [Collective-Use Computer
Centers] and data transmi.ssion systems, an important role is played by the proh-
lems of topologic design, as a result of which the locations of the VTsKP, con-
centratoxs and multiplexers must be determined, the general com~unications network
structure synthesized, and its characteristics de~ined. The long duration of the
period of creation of the VTsKP network and also the variation of a number of
initial design param~eters in the time interval from development to introduction
determ~ne the necessity for transition from traditional static network design
problems to dynamic ones.
In the dynamic problem it is necessary to find the plan for development of the
VTsKP network and deteYmine the sequence of structures of the developed net~aork
for which ma:cimum effect from its use will be insured.
I?ynamic Problems of Desi;ning Centralized Networks
Let us consider the statement and mathematical model I of the dynamic problem of
- designing centralized networks.
Given: the set :C-{Y~}, j=1,n is the subs cribers of the network the sources of
problems; the geographic coordinates of each su~scriber are {~~,w.}; the predic-
tion of the variation in demand for infor*nation-computation operai~ions (IV) is
_ h�(t), t~[t~,T), where t~,T are the times of beginning and ending ~perations
o~ creating the network; ~proc~t~ Ctrans(t,h) are the forecasts of variation
in cost of information processing and transmission, respectively, with the course
of time; the number of steps in creating the network is K; ca~ital investments
are Wk allocated Eor creating the network in the k-th step k=1,K. It is necessa
to determine the plan for network development and find the series of structures
D1, D2, Dk for which the following is ins ured:
K (1)
max Ha (Dti I~ 1~-t)
f=~
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~~cik ~?F~hi~ i,~i. ~ ~,r ~?n~.i
~mder ttie cunditions
~~~~tilDf-~~~w ti~ . ~s+~x, c2~
y; a11oc
Ke 1. ~~Dk) S fi.~P(tlic), j=l.R, ~3)
Key: 1. req .
(4)
- E-la~D~C~D~-l~~Na(Dic-1~i e~a ~~k~~k-~~ ~
~
Ha~9k~" ~ ~i C~k~s
where Ha(Dk/Dk_1) is the total volume of IVR performed by the network in the k-th
step; ~J~(Ilk/Dk_1) are the required ca~etal inveatments on converting from the
Dk_1 structure to the I1k structure; h. 4(t~)~, h.(Dk) are the required and actual
automated volume of IVR of the j-th s~ubscriber ~n the k-th step, respectively,
j=1,n.
In order to solve the dynamic problem (1)-(4) a basic recurrent relation was found,
and a calculation algorithm was developed that uses dynamic programming [1].
A more general statement of the dynamic problem (model 2) is also possible, in
which the general means of creating the network WE are given, and it is required
that they be distributed in the best way between the stens and the series of struc-
tures D~, D~, Dk be found for which (1) goes to the minimum under the condi-
tions K
~W~(~~/De-i): Wz.
t=~
A two-level dynamic programmir~, algorithm has been develgped for the dynamic model
2: the optimal distribution o� means among the steps {Wk} is found on its upner
- level, and on the lower level is the opti~al distribution within the step between
the corresponding VtsKP and centralized commimications networks. Thus, an embedded
dynamic programming process is used to solve dynamic problem 2.
Dynamic Problems of Centralized Network Design
In contrast to centralized VTsKP networks, distributed networks are characterized
by complexity, multiconnectedness of structure, uniqueness of paths of flow dis-
trib ution. The prob lems of analysis and synthesis of networks of this class are
described in terms of the "multiproduct flows."
- Let us consider the dynamic model of the desi~ of the structure of a di~~t~iouced
ne two rk .
Given: the matrix of request H(k)=~~hi~~k)II~ hii~k) is the required magnitude of
information exchange among the network ~~ctions i and j in the k-th step; vi1'
is the relative cost benefit from information exchange between junctions i and j;
M(k-1) is the network structure in the (k- 1)-st step which is ch aracterized bv
the presence of effective communication channels (i,j)f~,M(k-1), their carrying
capacities di� (k-1) and achieved output capacity of the GTsKP TIi(k-1) .
Required: to~find the matched plan for development of all VTsKP and the structure
of the intercenter SPD M(~.), for which the ma~mum effect E from using the network
56
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in the k-th step is insured with a restriction on the allocated capital investments
wk alloc' T~e ~thematical nodel of this problem has the form
~,ox E(N4(~?)snu,x ~~,rL~~. j (M(~)~ri(~-~)) (5)
~e
under the conditions
~ j (~C)s (~C1. ~6~
~.~ry ~ y ` fl ~ , ~
m
w~(n~~y~M(~-i1)=~ C~ ~~~(~~/n~~ C~-t~~~ cs~
c ~ P
'~t.c~cn(~) 2c ~M(~l/M((c-i)~ , W { ~2~'.
Key: l, trans; 2. alloc; 3. process
where ~iProcess~Ti(k)/~I. (k-1)) a.re the required expenditutransor increasing the
output capacity of the ~ITsKP to the magnitude of 1Ti(k); CrQ (M(k)/M(k-1)) are
the e:cpenditures on increasing the carrying capacity of the channel (r, 2);
-~i~ is the specific labor intensiveness of handling the traffic hi~.
As a result of analysis of the model (5)-(8) it was established that in contrast
to the model (1)-(4), for model (5)-(8) the condition of additiveness is not sat-
_ isfied. This excludes the possibility o.f using the c;~ethod of dynamic prograIIUni.ng.
Inasmuch as in full, the problem (S)-(8) cannot be solved strictly, the
following simplif~~ing assum{~tions are introduced for its solution:
1) The principle of priority in development of the network is introduced which
means that during synthesis of the developed network, the apnearance of only
those commLmication lines which must be used also in the final topology of the net-
*aork is permitted;
2) In each k-th step not all of the centers are developed, but only some subset
of them Y(k).
The method of solving the dynamic problem (5)-(8) includes two procedures.
Procedure 1 consists in determining the subset of VTs [con.~uter centers) which
must be developed in the k-th step Y(k) and finding the traffic ha~(k), transitVOn
of which will insure the greatest effect. For this purpose, the e:tponent vi~/C-,
is used where vi� is the effect from transmission of the traffic h, c�. is ttle
ij 1~
- sum of the e:cpen~ditures on transmission and processing of the traffic hij. Then
tne perimeter e:cpenditures Wi(k) on development of. the i-th VTsICP and the value
of W(k)=~ Wi(k) are determined.
i=1
Frocedure 2. The remains of the means for developroent of the SPD are determined
_ ~~trans after ahich, using the values found for {hi~(k)i, we solve the prob-
lem of optir~.al selection of the carrying capacity (VPS) by the criterion of the
minim~n C..trans or T
me an '
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~�vn vrr.. ~n., v.~c. .,i....
The presence of undefined initial data and also several criteria in the net4iork
design nroblems dete nnine the expediency of using the dialog mode. The applica-
tion of the dialog mode insures the possibility of combining powerful mathematical
methods and unformalized knowledge of the designer in a single process. For
realization of the dialog mode, a dialog system ~aas developed for tapologic optimi-
zation of networks DIATOS j2] based on the BESM-6 computer and the UOOGI graphical
display.
The svstem software consists of functional and support subsystems and a control
program. The functional subsystems include the optimization subsystems, sub-
systems for analysis, correction and input-output. The optimization subsystem
includes operating ~rograms for optimal location of the VTsKP and KD, optimization
of the network topology, and so on; the analysis subsystem permits calculation of
tne basic operating indices of the network, the correction subsystem offers the
possibility of introducing changes into the outgoing and intermediate data and
also the dvnamic structure using a light pencil.
The interactiun between the designer and the system is realized using the system
input language.
The DIATOS system permits realization of the interactive mode when solving dynamic
PrsKP network design prob lems, significantlv expanding the possibilities of the
operating optimization programs. In particular, the following problem is investi-
gated.
Let it be required to determine the optimal plan for the development of a central-
ized network in model 2 where~the capital investments WE are variable, and let it
be necessary to find max(1/K)k_1Ha(Dk/Dk-1)-~x Emean ~der the condition
W~-*min.
Both criteria E and W~ are opposite with respect to effect, and it is
necessary to findaa compromise solution satisfying both criteria simultaneously.
The procedure for finding the compromise solution in the interactive mode consists
in the following.
1. Let us determine the range of possible values of WE: ~W~n' Wmax~'
2, Let us give the initial value of ~aO-W ax~ let us solve problem 2 with respect
to one criterion ~ax Emean~W), and find t~ie values of (E~an~~~' ~~0~'
~ 3. Eeing given the admissible discount ~~J and setting Wl=W~-~W, we again solve
the problem with respect to one criterion W~ E~ean~ and let us determine the
pair of values {Emean~l~~ W~(1)}. 1
Analyzing these values, the desi~er.:nakes the decision either to continue
the optimization process or curtail it. as a result of repetition ofandeWs 3, 4,
a compromise curve is constructed in the plane of the criteria Emean
_ On tnis curve, using some additional information (for example, the condition
'Emean~~~J~~min), the designer finds the most appropriate point.
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On the basis of the propo:~ed algorithms for solving dynamic problems, programs
for designing the developed networks of VTs (models 1 and 2) on the BESM-6 have
been developed which were used to solve some of the practical problems. In
particular, the application of a dynamic :nodel when designing the Latvian SSR
network made it possible to increase the average network output capacity by 11%
as compared to the static model.
On the whole, realization of the proposed dynamic models permits solution of a
theoretically new class of network design problems in which the initial data and
parameters are variable, and the use of the interactive mode insures the possibil-
ity of considering the multicriterial nature of these problems.
BIBLIOGRAPHY
1. Zaychenko, Yu. P. "IJynamic Problem of Controlling VTs Network Development,"
ITPRAVLYAYUSHCHIYE SISTE;tY I r1ASHINY [Control Systems and Machines],
No 6, 1978.
2. Zaychenko, Yu. P.; Kondratova, L. P.; Pechurin, N. K. "Dialog System for
Designing the Structure of Collective-Use Computer Center Networks,"
UPRAVLYAYUSHCHIYE SISTEitY I MASHINY, No 3, 1979.
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ruK ~rr~~~wi, uar. ~�~?.r
AN APPROACH TO OPTI~IIZING THE STRUCTURE OF A LARGE-SCALE DATA TRANSMISSION NETtJORK
[Article by G. P. Zakharov and V. V. Lokhmotko, Leningrad, pp 57-61]
The traditional approach to the solution of the problem of structural optimization
of a large-scale PD [data transmission] network on arbitrary weighted graphs turns
- out to be in practice unrealizable because of the absence of sufficient decoiuposi-
tion experience and limited possibilities of the computer equipment used. A method
of automatic calculation of the structure of a large-scale PD network in the class
of imiform and regular graphs is proposed which permits significant reduction of
the size of the model and realistic optimi.zation of a large network witho ut losses
to the basic qualitative properties.
A characteristic teature of the proposed apnroach which con,siders a PD network in
the form of a set of two subsystems (delivery of inessages and technical mainten-
ance) consists in the possibility of coordinating the economic indices of the net-
work, its structural parameters and also ~he probability-time characteristics of
the processes of delivering messages and technical maintenance within the framework
of a single mathematical model, which permits recommendation of it not only for
selecting the hardware for equipment of the network and topological optimization
in the initial design phases, but also when solving the problems of structural
network control.
The initial data for the calculation are as follows:
N-- the number of terminal stations of t1e network (OP) with a breakdown by
a tYPe~
\F the specific intensity of the outgoing traffic from the OP of the ~-th type;
v information aging intensity;
V volume of inessage;
~b, ~p jtmction and network load closure coefficients reflecting the nature of
uniform gravitation between OP;
kk, k3 the coefficients of the efficiency of use of the communications channel
(~S) and switching center (L'K) (concentrator);
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zl, z~ dimensians of the rectangle approximating the territory;
p-- types of concentrators and UK distinguished by output capacity {Gi}~
cost {ci} and reliable indices (availability factor {kri} and recovery
intensity {ai});
q-- types of KS distinguished by PD speed {C.}, the coefficients {a�} and {b.}
of the cost functian of the line equipment ant~ also the reliability indices ~
{kr~ } and {d~ } ~ .
g-- types of technical maintenance centers (TsTO) distinguished by functional
accessories and annual expenditures on maintenance {eY}.
The dependence of the KS reliability on length kr~(~.) is proposed.
It is required that the reduced expenditures function TI taking into account both
capital expen ditures of introduction of the network K and operating expenditures 3
be minimized:
ncC'N`( t 3 Mi/L
~ ~1~
on satisfaction of the restrictions on the average time T and probability of
timely delivery of inessages Q. In particular, it is necessary to determine:
The number of steps in the network hierarchy (R);
Tne type of structure, types of UK and KS in each step;
Number of UK (n), KS -(m) and TsTO -(h) in each step.
It is proposed that the integral model of the network structure be represented
in ~he form of a set of three functionally distinguished models.
1. Models of the estimate of the probability-time characteristics of the PD
network fo r different switching t2chniques [1,2,3 and so on], giving the
analytical function T(a.,u, kr, d, k30) and Q(a,u,~, kr~ d, k30) where a and u
are the intensity of the incoming flow and intensity of servicing the UK (KSI,
respe ct ively.
_ 2, Models of estimating the efficiency of technical maintenance permitting
determination of the probability of servicing the next hardware set without wait-
_ ing k30 (4] as a ftmction of n, kr, d and h..
3. The topolo~ic model developed by the authors based on the concept of a contour
R-separating graph with simple subordination [5] integrating the hierarchical
structure by a composition of subnetworks of different levels. Here the snectrum
of possible topolo~ies is quantized by a set of base graphs, including the null
graph, the sh ortest connecting network, radial, lattice and uniformly S-connected
2105, the choice of co~~nunications hardware to equin them and
discovery of the most effective regions of application of various switching
me tho ds .
The results of the studies demonstrated that the proposed approach to optimizing
the structure af a large-scale PD network is an effective means of decision making
on the part of structural organization of prospective networks.
BIBLIOGF.APHY
1. Zakharov, G. P. SETI PEREDACHI DANNYKH (Data Transmission Networks], Part l,
Leningrad, LEIS, 1976.
2. Zakh arov, G. P. "Data Transmission hetworks with Packet Switching," VOPROSY
KIBERNETIKI [Problems of Cybernetics], Moscow, 1979.
3. Zakharov, G. P.; Lokhmotko, V. V. "PD Network with Packet SwitchinR
Operating Over a Virtual Ch annel," TEKH~~IIKA SREDSTV SVYAZI [Conununications
Hardware], TPS Series, vo 4, 1979.
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hoEman, a. ; I~n�uon, R. ~t~1SS~~~'OYE OBS'.UZHIV~1NIlE, TEORTIA I 1'l:ILO?k[EN11'A
[Queueing. Theory and Application], ;Ioscow, Mir, 1965.
5. Basaker, R.; Saati, T. KONECHNYYE GRr1FY I SETI [Finite Graphs and Networks],
Mos cow, Nauka, 19 74.
6. Kleinrock, L. KOMMUNIKATSIONNY:'E SETI [Communications Networks], translated
from the English, Moscow, vauka, 1970.
7. Pashkeyev, S. D. ;~Iinyazov, R. I. ; ~iogilevskiy, V. D. MASHINNYYE METODY
OPTIMLZATSII V TEKHNIKE SVYAZI [P~fachine Methods of Optimization in Communica-
tions Engineering], Moscaw, Svyaz', 1976.
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TIME DECOMPOSITION OF AN AUTOMATON
[Article by L. N. Zorevd, V. G. Lazarev, Moscow, pp 61-62]
:~s a result of complication of the operating algorithms of digital automation
devices and computer engineering, the necessity for varying the algorithm during
the functioning of the digital device, the problem of constructing logical control
units (LPU) with adjustable structure combining the advantages of ULU with hard-
ware and software execution of the operating algorithms, is acquiring more and
more urgency. This article discusses one of the automatic models of ULU with
adjustable structure in the form of time decomposition of the auCOmaton A, and its
implementation principle is considered.
Let the automaton A be represented in the form of a composite of subautomata
A1,...,A4. Then the decomposition of the automaton into subautomata A1,...,A4
will be calle3 a time decomposition if eny internal state K~I~K~,...,KS~} of one
and only one subautomaton A�EfA1,...,A4}such that the transition function d~
and output functions a. of ~he subautomaton A~ when it is in the intemal state Ki
assumes the same values as the transition function 8 and output function j of
the automaton A when it is in the intemalstate ~ci, is compared with any internal
state K1E{K1, .,.,~cS} of the automaton A.
Thus, in contrast to the known types of spatial decompositim of the automaton in
whicl: each internal state of the automaton A is representable, generally speaking,
- bv internal states of several subautcmata, during the time decomposition each
internal state of the automaton A is representable by an internal state of one
and only one subautomaton A~.
Obviously, the time decomposition of the automaton, just as the spatial deco~osi-
tion, can be interpreted as a special encodinQ of the intPrnal states of the
automaton A. Some exa~les of the coding of the internal states of the automaton
A corresponding to the time decomposition of the automaton are considered.
On the basis or deternination of the time decomposition of the automaton A, if
the automaton A at the t ir~e t mus t be in the internal s tate K(t) , only one of the
subautomata A�E{Al''",A4J will be in the "excited" state., in the internal state
K~(t) which i~s compared with the internal state K(t) of the automaton A.
- It is easy to understand tl~at the time decomposition of the automaton is a break-
down of ~he set of its internal states into n nonintersecting subsets, with each
of which the subautomaton A~E{A1, .,A4} is compared.
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_ ruK urr~~iw~ uar, v~vLr
~?rte ~f the ~riCaria ~f brcal:Jot.�ti th~ ~~C ~t .Lutarnal ~tat~~ ~t tha ~uw~uat~~u :1
into subsets can be the "connectedness" of the internal states by transitions,
outputs, and so on.
A discussion is presented of the method of formation of the groups of connected
internal states based on the method of obtaining maxim~ groups of joint internal
states of the automaton, and a procedure is presented for constructinR the time
decomposition of both the general type automaton given in the language of the
transition tables and the microprogram automaton given in the language of logical
flow charts of the algorithms.
Considering noncomparison of the operation in time of individual s ubautomata of
decomposition structure of the automaton each of the subautomata can be realized
at different points in time in the same segm~ent of uniform medium of the progra~a-
ble logical matrix o-r in another basic module permitting rearrangement (reprogra~ing)
~ of its structure.
This realization of the time decomnosition of the automaton with respect to parts
using the same reserves is essentially th~~ hardwar~software implementation of the
- automaton and is a generalization of the known principle of cycle-by-cycle imple-
mentation of the automaton.
The structure of the device for hardware-software implementation of an automaton
is presented.
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I~()R ()N'F'I('IA1, l1SF: ()N1.Y
DISTRIBUTED CONTROL IN SWITCHING CENTERS USING MICROPROCESSORS
[Article by 0. N. Ivanova, rtoscow, pp 63-67]
The problems of optimal synthesis of the control units of switching offices and
centers of co~tmications networks are an important problem, the solution of which
determines the technical-economic indices and expenditures on technical maintenance.
In their development the structures of the control units have gone through a r~um-
ber of stages which were characterized by the element base for implementation of
the control units (L'U), degree of centralization of the W and switching equipment
sys tems .
In the ten-step ATS; individual relay type control units are used for each switch-
ing device. The complexity of the W was determined by the functions of the switch-
ing device in the corresponding finding steps. In the crossbar ATS, relay con-
trol units are used for a group of_ switching devices which form a switching mod-
ule. The complexity of the W was determined by the parameters of the switching
module and its ftm ctions (conditions) in the corresponding finding steps. The
transition from individual W to general W using the same element base, that is,
relays, limited the volume of switching devices which can be serviced by the W
on rhe basis of low operating speed of the relays (12-30 milliseconds) . Therefore
each Einding stage was constructed from individual switching modules, each of
which was assigned a w� In addition, the volume of switching devices which were
serviced by one W also depended on the operating speed of the switching devices
themselves during the process of setting up a call inasmuch as the i?U
could simultaneously setting up only on? call within the limits of the Qiven
module. The time of incluaion of the switching eletnents on the connecting path
from the module input to its output was on the order of SO milliseconds
~tmean VM+'tmean UM~' The effort to increas e the degree of centralization of the
UU in order to decrease their nim~ber could be realized only on a new electronic
basis. With the appearance of semiconductor transistors and diodes it became pos-
sible to use this element base to construct the UU of automatic telephone offices
and centers. This element base ~ame to be called circuit-board electronics, in-
asmuch as when installing the UU each element was a separate component of the net-
work. The appearance of electronic L'U opened up a new area in switching engineer-
ing with the b uilding of inechanoelectronic ATS (MYe, Hungarian offices. PS-KE-100,
and so on). However, in these ATS systems it was not possible to make fu11
use of the speed of the W to signiiicantlv increase the number of switching
devices se rviced by one UU inasmuch as the switching devices themselves did not
have the necessary speed.
- ~autumatic telephone oEficej
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Fl)R l)NF~IIIAI. USH; ONI.Y
"i'he broad possibilities opened up by high-speed electronic W making use of pro-
gram control led to finding a new element base for constructinQ the switching
system of the ATS, the b asi c requirements were good contact quality in the
information transmission channel and high speed during the process of setting up
and terminating calls. This element base was provided by hercon relays
~tresponse-2 milliseconds, t elease-0.5 millisecond), the ESK relay, ferrides and
hesacons. The combination of the switching system constructed from hercon relays
or the above-enumerated relays with electron control units led to the development
of quasielectronic switching offices and centers. These systems include the
ESSI, IOC, IOR, "Kvarts," "Kvant," "Istok" and other systems.
In these syste~s the W were constructed on a new electronic base integrated
microcircuits which ins ured an increase in operating reliability of the W,
simplification of the installation of the UU, and a decrease in size. In
the quasielectronic ATS, the degree of centralization of the W is appreciably
higher than for the mech anoelectronic ATS. Especially for the first models of
- quasielectronic ATS in which all the functions of setting up calls, recep-
tion and processing of the address and control information were invested in a con-
trol computer (EUI~i), the output capacity of which would be sufficiently hiqh with
high ATS capacity (250-500�103 op/sec for an ATS with a capacity of 10,000 to
20,000 nunbers). Thus, at that time the structure of the UU went from the
_ individual W to the centralized, all-office device which provided control of the
- switching devices within the limits of the entire switching system (KS) of the ATS.
The high degree of centralization of the 'JU significantly increased the requi.rements
on the operating reliability of the L'U of the ATS, for failure of the UU led to
shutdown of the entire ATS. Therefore special meas ures were taken to improv~~ the
operating reliability of the W such as redundancy, deep monitoring and diaglosis
of the equipment, ~ahich required both increased capital expenditures azd incr~eased
output capacity of the W inasmuch as the monitorinQ and diagnostic programs
account for 40 to 60% of all of the instrsctions executed by the EUM during ~ts
operation. After appearance of the. quasielectronic ATS with high degree of central-
ization, deficier.cies were discovered in this method in which it is necessary to
include the following. With an increase in capacity of the ATS, it is necessary
simultaneously to increase the output capacity of the EUM, wtiich leads to the
necessity for implementation of it to use the element base with hiRh speed, and
consequently, it leads to an increase in cost of the EUM; the req uirements on the
reliability of the operation of the EtM increase.
For elimination of the first deficiencvf =he call set-up algorithms were execut~d in
parallel so that part of the processes would take place in parallel, but this,
in turn, complicated the general algorithm because it required dispatching when
executing indi vidual pro~rams, establishing situations of conflict with simul-
taneous reference to common modules (for example. the readv-access memory) and
introduction of a large ntnnber of interrupt levels.
In addition, in order to decrease the influ~ence of the low speed of the KS and
terminal sets, part of the EL'M functions were transmitted to peripheral W(PW)
which could interact with tne systems and KS without direct participation of the
EL'M and transmit information to it or receive it on instruction from the EUM.
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Thus, the structure of LTU with distribution of functions with respect to
individual modules of the control wiits appeared. This method of construction
made it possible to lawer the requirements on increasing the output capacity of
the EiJri, because part of its functions began to be performed by individual PUU
which can be both passive and active.
In this method of construction, research is req ui red with respect to optimal dis-
tribution of the functions among the individual modules of the PUU and the EiJM
itself and also synthesis of the modules realizin~ the given function. Then it is
necessary to develop the software for the entire W for the p,iven type of office
considerin}; auxiliary types of servicing, automation of technical maintenance
and a number of other ftm ctions.
:~todern progress in the field of electronics and the creation of a new electronic
base on the basis of large integrated circuits (BIS) and microprocessors (riP) is
opening up new wa~s to synthesize the UU of switching offices and centers.
Large integrated circuits can cariy out q uite comnlicated functional problems
during the process of controlling the setting up of a call and can be a
device for hardware i~lementation of the control functions.
In the ATS switching system or the switching system of a center it is possible to
isolate operations with respect to s e t t i ng up c a 1 1 s which are repeated
for each c a 1 1, and they are performed independently, receivl.ng only the
instruction to execute and the instruction to output the results of execution
from the computer if needed for subsequent operation of Che UU. If such opera-
tions are encountered in different parts of the system, they can be executed by
different BIS, the operating priority of which is given by the operating program
of the EUM with respect to settin~ up the ca11.
If it is necessary to perform different operations, it is possible to ~ise micro-
processors, each of which operates by the corresponding program. Here we have a
set of ~tP, each of which carries out its mission, their operating priority is
provided bv the EL~t which can be e:cecuted in the form of a minicomputer with
integrated processor ~ahicn, in turn, can also be executed in the form of an
With this method of construction, the UU will be a set of BIS and MP providing
for the e:cecution of all functions of controlling c a 1 1 s at the ATS or
center, b ut each BIS or :a' will be connected only to part of the KS eq uipment or
sets, that is, the control will be distributed somehow ove- individual modules of
the switching equipment and the ATS svstems. Here the primary principle is the
princinle of control distribution by which failure of one BIS or MP or another ~.~{.:LL
not disturb the operation of the A~S.
Obviously it is possible to find distribur.ed control structures which will reflect
the same structural redundanc~ as the KS where the connection from the input to
the output of the RS or an indi~,~dual module of it can be provided by several
connecting paths from which one is selected. Failure of one path does not lead
to disturbance of the possibility of settin~ up calls but only lowers the
qualitv of servicing tne calls somewhat with respect to time required t:. eliminate
f.ailure if it coincides :oith the PLH [peak load hours]. tidith this structure,
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the necessity aris~s tor investi~;a[ing the capabilities of the manufactured BIS
and ~fP to solve individual control problems at the ATS, to optimize the structure
of the W based on 3IS and microprocessor sets and to develop software correspond-
ing to the operating requirements at the ATS or center. The use of distributed
control is possible both in the quasielectronic ATS and in the EATS implemented
on the basis of digital data transmission. In the digital systems of the ATS,
the switchin~ system will be executed by means of electronic contacts which, in
turn, can form electronic connectors for the required number of inputs and the
number of outputs m realized in the form of one BIS. Such connectors, forming
individual modules of the ATS switching system, can control the functional modules
of the W which can be realized by means of the MP operating with the given
aloorithm for the given switching module. Individual sets (or groups of sets) of
_ one type or another (AK, ShK, SK, RSL, and so on) can also be implemented on the
basis of the MP and the BIS.
Inasmuch as at the present time the BIS and the MP are primarily created for the
circuitry of computer engineering, it is possible that they do not fully
corresp~~nd to the requirements which are imposed by the ATS control units; there-
fore the question can be stated of creating specialized BIS and MP for the UU of
the switching centers and cffices. For this purpose it is necessary to develop
circui try for the BIS and MP which will to a ma~m~ degree satis fy the require-
ments on the W structure.
In the switching equipment the number of 3IS and MP required to construct the W
is quite large; therefore the production uf specialized BIS and MP in industry
can be .~ustified economically. The problem of the developers is to create
universal BIS and MP for co~unications engineering which can be implemented in
industry.
The layout of an ATS with a capacity from 2048 to 8192 numbers of the quasielec-
tronic type is considered in which the subscriber Einding stage inplanented by three-
link BAL modules with parameters 2048x1024x512x512, the group finding stages using
BSL modules with parameters 512Y512~512~d~~p~ ~3~
Key: l. threshold
where L=1,2,3,... which corresnonds to quasistatic control.
The general state of the net~aork is estimated at the TsUS on the basis of the
matrix D(t) with the elements di ~(t). The shortest path is found using a mettiod~
for. e:{ample, the dyndmic programm~ng method. Here not one, but n shortest pattis
are defined. Let :~k . denote the k-th path of the investigated paths joining the
j~mctions i azd j. 1~'~r this path the delav will be
k
T"~~t~ t~~n;~dw.~(~). (4)
The value or (4) is calculated for a11 n routing versions and the values of Tk (t)
are compared to each other. If one value is distinguished from an~ther bv l,j
less than some amotmt control is realized by the switching center control sub-
svstem. For e:cample, the method of dynamic priorities car be used [9], where the
- info rnation distribution p1an on the network does not change. In the opposite
case the Tsi'S selects tne shortest path and corrects the information distrib utior~
plan. The nature of the solutions adopted when using the given method can be
- demonstrated in an example where the number of paths between the i and j jun ctions
from which it is possible to ctioose is n=~. At the TsLS, the delavs are co~npared
with respect to these paths and
if T~~A(t)c T`-e~t~-d ~ then ~ ~,~~t)=A
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PVt~ VCr~~.ir~?. v..~a: ~i~~~.�
if T ~t)< T i~~~(t)-d then ~ i..j ~t)" g~ (6)
if ITK~~ t _ then ~ . ~t)= A.6. (7)
~ ) T (t) ~ ~ d ~ ,d
Thus , in the cases (5) and (6) the routing is selected on the TsUS, and in the
case (7), the path is chosen at the switching center on the basis of the routing
matrix developed in the network design stage. The para~eter d determines the
degree of independence of the switching junction. If S is small (that is, even
~nsignificant changes are considered in the delays with respect to different
paths), we arrive at a fu]_ly centralized control. If d is large, we arrive at
decentralized path sele~tion. Exceedir.g some threshold by the average delay with
respect to the entire network indicates overloading of the network with messages.
In this case the TsUS goes to the load limiting algorithm, for example, curtailing
access of low-priority messages to the network or using other load limiting
- algorithms [4~.
Thus, imF,lei~ntation of the discussed method permits the use of the advantages of
decentralized and centralized methods of constructing the control subsystem. In
additic~n, the given method permits efficient use of the control subsystem in the
entire range of load variation,
c?ne of the primary difficulties in implementing any nontrivial method of dynamic
traffic control on a commimications network is the fact that the "operation" Q(t)
is distributed in space and time. In other words, the special. operation Qi~~ (t)
is known exactly only at the time t and only at the jtmction i. Information about
Qy (t) can be transmitted to another junction, but this information can become
obsolete during ~ransmission time. Thus, any global characterization of ':he
- general operation of the network Q(t) is ~ased on data pertaining to the past
and not current information about the state of the jtmctions. In the network
there are ~~ro types of information about its state:
Precise and timely local information (that is, information abouC the state of the
switching center at the same center) . This info~cnation is available for every
- center;
AveY~ge values describing the past local characteristics of the network.
The prooosed dynamic cuntrol method permits full use of both types of information
abotit the state of the network, which insures effectiveness of it.
BIBLIOGRA.PHY
1. Searobinets, S. ~t. "Study of the Efficiency cf L'sing Bypass Paths in the
Presence of Dynamic Control on Channel Switching Networks," author's review
o~ candidate's dissertation, ~ioscow, 1977.
2. ~leinr.ock, L. VYCHISLITEL'YYYE SISTE1tY S OCHEREDY~MI [Computer Systems with
Queues translated trom the English, Moscow, Mir, 1979.
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3. Naylor, Td. F. ; Kleinrock, L. "On the Effect of Periodic Routing Updates
in Packet-Switched Networks," i~ITC76-NAT. TELECOM. CONF., New Ydrk, Vo1 1,
19 76 .
4~ Kazachenko, Yu. M. SOVREMEDlNOYE SOSTOYANIYE I PERSPEKTIVY RAZVITIYA
SISTEM UPRAVLENIYA POTOKAAQ INFORMATSII NA SETYA.KH SVYAZI [Modern State of
the Art and Prospects for the Developraent of Informatian Flow Control Systems
on Co~unication Networks], Leningrad Electrotechnieal Communications
- Institute, Leningrad, 1979, 56 pages, 94 references, manuscript deposited
at the TsNTI "Inforn~svyaz' 18 July 1979, No 24.
S. Beloborodskaya, T. V. ; Solodyannikov, Yu. V, "Organization of rieasurements
on Packet-Switched and Message-Switched Computer Networks," ZARUBEZHIIAYA
RA.DIOELEKTRONIKA [Foreign Radio Electronics], No 3, 1978.
6. Butrimenko, A. V.; Lazarev, V. G.; Sergeyeva, 0. F. "Problems and Architecture
of an Automated Communications Network Control System," POSTROYENIYE
UPRAVLYAYUSHCHIKH USTROYSTV I SISTEM [Structure of Control Units and Systems],
Mos cow, vauka, 19 74.
7. Bershteyn, P. V., et al. "Structure and Construction of Telegraph Network
Control Systems," TRUDY TSNIIS [Works of the Central Scientific Research
Institute of Communica~ions], No 6, 1977.
8. Rudin, H. "On Routing and Delta Routing: a Taxonomy and Performance Compari-
son of Techniques for Packet-SwitchPd Networks," IEEE TRA.NS. CGt`iMUN.,
vo l, 1976, Com.-24.
9. Pickholtz, R. L.; McC~!v, C. Jr. "Effects of a Priority Discipline in Routing
for Packet-Switched Networks," IEEE TRANS. CO~tU:~1., No S, 1976, Co~24.
~ 79
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H'l)R l1hMIl.1AL U,~ uivLr
SELECTING TYPES OF PROCESSORS FOR A MULTIPROCESSOR SYSTEM
(~rticle by A_ N. Kol'tsov and F. I. Pepinov, Moscow, pp 75-77]
A study is made of a multilevel hierarchical system w~ th given structure. The
apexes of di,f ferent level joined to each other form a precursor -follower pair.
In the k-level system the i-th apex of the R-th level forms the set Fi of its
followers of the ~.+1 level and the set Fi`` of its follawers from 2+1 to k level.
This system can be a model for execution of a parallel computation problem,
administrative relations and the relations of any agency, a multiprocessor data
processing system, control unit, and so on [1]. Beginning with the selected
structure of the system and its purpose, a special algorithm Qi is matcned to
each apex of the system i in some way or another. This special algorithm is
executed by s ome type of processor from among the given ones located at the i-th
apex of the system. The composition of the special algorithms Q={Q1, �..,Qm}
is the operating algorithm of the system.
In the investigated system in the processor memory of the i-th apex, in addition
to the special algorithm ai executed on this proc*ssor, all special algorithms
6'~i matched to tne follower apexes from the set F i are stored (bu*_ not executed).
The special algorittim stored in the memor~ of the i-th apex processor can be
transmitted to the follower apexes from the set Fi.
The investigated svstem is implemented in a set of processors of different types
R=~Rl, RL.1}, The types of processors 3~ , j=1, ��.,n can differ significantly
with respect to their capabilities; therefore each special algorithm Qi, i=1, ...,m
can be executed on one type of processor ~7r another with different speed, relia-
oility and cost. The e:cecution of ~i on R~ is characterized by the following
parameters o f the special algorithms and ~rocessors.
CJ� is the cost of the j-th type of processor; is the intensity of failures
of the j-th type of processor; t. is the given execution time of oi; Li is the
magnitude of the penalty for fai~ure to execute the algorithm ai; Vi is the
magnitude o~ the penalty for exceedinQ the execution time of the algorithm Qi
per unit time; pi]� is the probability of failure to exec~te the algorithm ~i when
executing it on the j-th type orocessor; ci~ is the cost of developing a metnod
of implemenring the special algorithm ci on the j-th type pro~~ssor; ti J is the
time of e~:ecution of ~i on the j-th type of processor.
80
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The enumerated parameters will permit determination oi the magnitude of the
average losses ~lii� when executing the algorithm csi on the j-th type processor
which is ~ade up of the following components:
c'i is the cost of e~cuting the algorithm csi on the j-th selected type processor,
c' i~=c~+c �
ij'
Lipi. is the average magnitude of the penalty for failure to execu~te Qi, where
the ~robability of this event is calculated by the formula:
-a; t ~1
P~~' ~-e ,
V.t'� is the penalty for exceeding the execution time of the special algorithm
Qi by~the time t`i~ which is calculated as follows:
, 0, i f t~~ ~ t;,
` ~ -if ti,>t`,
{ `1 = t - t
The magnitude of ~he average losses ~yij when executing the special algorithm 6i
cm the j-th type processor is calculated by the formula:
~';~=L;P~~ +v~~t:~+~~.~. (1)
I'he magnitude of the average losses in itaplementing the entire system:
T \
~ = ~ 2 /
It is obvious that the magnitude of losses ~y depends on which type of processor
is used to execute each of the special algorithms 6iE~.
A method of selecting the types ot processors esecuting the set of special
algorithms is proposed such that tne magnitude of the average losses ~ for i:he
given hierarchical multilevel system will be r.iinimal. Here it is remember that
- the number of processors in the s~stem is no less than the number of special
_ algorithms
rn t ~2~, (3)
J
where r~, j=1,...,n is an arbitrary given number of processors of the j-th type.
Othenaise, it is also possible to combine some special algorithms so that condi-
tion ((3) is met.
For each special algorithm ~J�E~7, values of the averaRe losses ~;~i~, 'Li2,. ��~'~in
are calculated 'oy formula (1~ for execution of the special algorithm on all
~iven tvpes of processors R, R~, R, that is, each algorithm ci has a
row oc losses ~~il~ '~'~,2'"''~in in correspondence to it. The set of such rows
Eorn~s a l.oss matrix each coluIIn of which is assigned an r~ - the number of
type R~ processors.
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N~UIZ UNNiIIAL UJC. u1VLti
On the basis of the loss matrix a matrix breaking down the special algorithms
with respect to types of processors B is constructed, the rows and col~s of
which precisely correspond to the loss matrix, and the elements are bi~, where
0, if Qi is not executed on the Ri processor
b..
1~ 1, if Ji is executed on the R~ processor.
Inasmuch as each special algorithm is executed on only one processor,
M1
~ ~ . ~ 4)
On the other hand, the number of processors of each type R~ is given, and this
means that
~ g~~ 5 Zd .
~ (5)
The e:{pected magnitude of the losses Y' for the entire system with respect to all
special algorithms is defined as follows:
- yr_ ~~~~~d�~~j1� (6)
J ~
The obtained expression (6) is the solution f unctional of the system, the minimum
value of which determines the choice of types of processors for the entire system
with the existing restrictions (4) and (5).
l
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- HOM~OSTATIC PRINCIPLE OF REGULATING THE OUTGOING SUBSCRIBER TRAFFIC
[Article by A. V. Kotov, Leningrad, pp 77-82]
Within the framework of dynamic traffic control on telephone networks, the volume
of the outgoing traffic from the subscribers can be automatically regulated. This
is extremely desirable from the point of view of increasing the cost effectiveness
of the commvnications networks [1, 2]. However, irrplementation of the indicated
_ regulation is possible only under the condition of improving the algorithm for
interactian between calling subscribers and the telephone system in which negative
feedback is introduced into the "subscriber-telephone network" control circuit.
The conversion of the interactio:t algorithm with introduction of negative feedback
into the telephone system is realized, for examQle, by certain additional types
of services such as the automatic answering device, "putting the call on hold"
and so on. These services decrease the number of repeated calls (PV) and thus have
an automatic regulating effect on the out'oing traffic from the subscribers. In-
asmuch as the largest number of PV on a network are formed as a result of low
accessibility of such GTS services as ticket ordering, the information office, and
so on, it must be expe cted that the greatest regulating effect with respect to the
occurring lo ad is provided by services which are designed to eliminate reje cts on
the part of the indicated services. An example of a hardware solution in this
area i~ described in [3]. Here the subscriber calling for service gets a recorded
message about the time by which he will r~~ceive a return call for se rvicing his
request. The indicated time depends on the number of requests accumu7.ated
previously for servicing.
As is known, in ordinary request and informarion servi ce systeffi the load is
characterized not only by the fact that it has a sharply fluctuating intensity,
but also by the fact that even during short-time ~.ntervals, for example, in the
plh [peak load hourl it does not have the prvperties of a simplest flow i.n view
of the presence in it of a large n:nnber of PV (a flaw with consequence). In con-
trast to this, in the svstem according to [3], the total load is somehow split b~;
the regulating me c'~anism into two flows: 1) a simplest flow (flow without PV)
with low intensity v �y consisting of the actual service requests
- occur m
cuming into ttie system in rea~time and having a constant service time (trans-
mission ot a voice message) ta ~(where ta e is the average b usy time in case
of ordinarv requests for information services~, 2) an ordered (deter~inistic)
clow of request servicing with a time shift ha vi.ng an ~ntensity y=const.
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F'l)N Uhhll.lAL U~~ UNLY
ylfl
y~nar
90
~ ~
~ I
0 ~
j ~
Figure 1
In order to explain the essence of the given regulation principle let us cons.ider
Figure 1 which depicts the load intensity distribution curve y=y(t) of the request
or information servi ce load for some time interval. The level yp denotes the
total carrying capacity of the entire operator staff (d~pending on rhe time of day
this level can vary in accordance with some schedule) . If the service is equipped
with a system according to [3], after a time tl all of the calls begin to be
ser~,~iced with wai~:ing. L'p to the time t2 (that is, while y>y~) the queue is en-
larged and after t2, it diminishes. The end of servicing with waiting takes place
at some time t3 defined from the expression
,~i t~
y~t~-y�~ dt "Jt ~y.-'~(t)]dt .
In Figure 1 this corresponds to equality of th~ crosshatched sections of Che area
above and below the curve y=y(t). A call coming into the system at the time t2
will be serviced with maximum waiting time Tm~ equal to
r wi(t), i= 1, p, where wi(t) is interpreted as the actual time spent
by the i-th priority request in the system. The value of the priority function
~i(t) is calculated by the Jackson formula [2]:
Si(t) = ui - wi(t).
The operation of the network is described by the following procedure. The direc-
tive time of delivery ui, i= 1, p is assigned to the messages entering a net-
work of i-th priority class. The messages are placed in a source-junction queue
in accordance with the priority function Si(t). The h~ghest priority corresponds
to the least values of si(t). After transmission of the i-th class messa&e to
the network it is stored for a time Ti (the waiting time for obtaining verifica-
tion of proper reception by the destination junction of the i-th class message).
- If on expiration of the time Ti verification has not been received, the message
is again transmitted. Otherwise the next message is transmitted with least
value of the priority function Si(t). The repeated messages reach the repeated-
message queue and have a relative advantage in servicing over newly arriving
messages.
Under the conditions of simplest flows of incoming messages with intensity ai,
i= 1, p, constant transmission time equal to a, independence of the repeated
transmissions, the basic expressions are obtained for the Laplace-Stiltjes
transformation of the transmission time distribution function in th~ network,
the average waiting time wi in the source-junction, the average transmission
time E[Vi] through the network of the i-th class messages for steady state of
the network.
~ Let Bi(t) be the distribution tunction of the random variable the time inter-
val from completion of inessage transmission to acknowledgment of receipt in the
transmitting junction under the condition that verification is delivered on time.
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The probability of the last event will be denoted by ni; then the probability of
repeated transmission is defined as vi = 1-~riBi(Ti). For E[Vi] the following
expression is valid:
T~
E~V~]�{a'J~[a+T~+S~(~1)a+T]+~L jtdB~(t)}~(t-a;,) ~1~
~
. o
where S'(1) _[Soqo(1 - z)/(0[z] - z)]Z_1 is the average number of inessages in
- P
the repeated message queue; Q(z) = E qkzk is the generating function of the
k=o
number of arrivals in the repeated message queue; qk is the probability of si-
multaneous arrival of k messages in the repeated message queue; T is the average
repeated transmission waiting time of a message from the repeated messages en-
tering the queue.
From (1), T* = T� is found the minimum average transmission repetition
time (it islroun~e~lto the nearest multiple of a).
For average waiting time Wi the following expression is valid:
(tJ:' Q~~(1) `
WY=uta+Q~(t~l c,,~~a*a~ z~�Q,~~~~1 t~,~~~t~ +
d'' ~2>
P ~-1
+ S ,Z~~uld -u.d+u.;,~ + ~la ~u.~'u'~)~ ~
d=~'~ d'~
where wo is the average time of completion of servicing equal to a/2.
The Laplace-Stiltjes transformation of the distribution function of the actual
' transmission time of an i-th class message is as follows:
i o0
n-l - ~no -~(n-l)`r~ ~ -sn~C P m _~u(!'_!) ~
= 5 J~ e e 6~(~)x; ~e ~ ~,e . q (3)
n=i k=p ~=1 m ~,1 n~,
T
where = f e-'tde~ (t), qID is the probability of arrival of m messages in the
0
repeated message queue, one of whir_h is i-th class.
The value of qm is found from the expression:
IlR~ L~.r ~~~r7Kt~K~'...~g0.T-SJ~~-,C~-~I[1nYKT1...~(~~~KP-1JKP'1~7
KE A (m- t, ~
m-1
where ~1(m - 1, i) is the set of combinations, the powers IA(m - 1, i)~ = Cp_1,
numbers 1, 2, n, p; n# i; k~ E K.
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- rvtt vrci.~ar~i, vn...
- The efticiency of the given control technique was estimated by simuZating net-
works ot two s[ructures distributed, consisting of 27 junctions, and a linear
5-junction network. The networks with and without control with direct servicing
procedure were compared by the following indices: the number of inessages deliv-
ered on time, the average delivery time and dispersion of the delivery time.
Under the conditions of uniform loading of the network with the control consist-
ing of 27 junctions, efficiency was demonstrated with respect to the criterion
of the average number of inessages delivered on time. For a linear network, the
range of loads in which control turned out to be efficient was obtained with re-
spect to each junction. In the indicated load range the effect is 5 gercent.
The following features are characteristic of the proposed technique.:
a) on satisfaction of the condition Si(t) ~ 0 the message is lost;
b) the param~`~r ui is not the only parameter for all requests (messages), but
it is in one-to-one correspondence with the initial priority, the urgency cate-
gory of the given request;
c) the priority function Si(t) of the request achieved in the given processing
stage (in the given communication center) appears as the final priority in the
next stage;
d) for Si(t) = T the request is assigned the highest priority with which the
i-th class request comes to all subsequent network reserves over its repetition
route. The interval T is interpreted as the network parameter and characterizes
the time required for the i-th request to pass through the network in the ab-
sence of control and loading of the network on a given level in the quasi-exclu-
sive mode of using the processing reserves of the network;
e) the initial and dynamic priorities are selected from the series: T, aT,
wT, where a, w are integral coefficients. Thus, all of them are multiples
of T, and each lower one is a multiple of the preceding higher one.
- Physically the efficiency of the control imposed on the network is based on in-
creasing the use coefficient of the network reserves most loaded at the given
point in time by expanding the period of their greatest loading in time as a re-
~ sult of the time reserve ui - wi(t) and use of the time reserve ~t = ui - t.
A study was also made of the laws of variation of priority in accordance with
arithmetic or geometric progressions or combination of them and also various
versions of organizing the time service. Analysis oE tt;e results of using dif-
ferent laws of priority variation demonstrated that in the majority of practical
solutions the use of arithmetic or geometric progressions gives saCisfactory re-
sults.
~aith programmed realization ot the enumerated versions it was considered that
the network junction has a separate program performing the functions of priority
control and monitoring of the time of existence of the message in the network,
ar.d the operations system has the apparatus for starting these programs after
time quanta equal to or proportional to T. The volume of the program e:�:ecution
14~
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for different versions turned out to be in practice identical: 25-SO instruc-
tions of the M-7000 computer, SM-1, SM-2 computers. The difference in versions
was discovered in the frequency of starting the programs and the required size
of the field for entering the achieved priority in the message title and the time
left before expiration of the control period.
The performed analysis of various versions of program implementation permitted
substantiation of the choice of prpgram implementation of the method of control-
ling message delivery on the switching level of a distributed operations system.
BIBLIOGRAPHY
l. Kleinrock, L. , KO~IIKiJiVIKATSIONNYYE SETI [Carmunicatiorr~'~etworks] , translated from
- the English, ~ioscow, .Iauka, 1970.
2. Jackson, J. R., "Queues With Dynamic Priority Discipline," MA,~AG. SCI.,
No 8, 1961.
3. Kleinrock, L., and Finkelstein, R., "Time-Dependent Priority Queues," OPER.
RES., Vol 15, No 1, 1967.
4. Silayev, V. N., "A Way To Control Queues in Distributed Data Processing,"
Finnish-Soviet Sympo~ium "Small Computers and Distributed Data Processing,"
Helsinki, Finland, 1974.
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r~~tc ~?rr~~ ~:~i. ~~;,r. ~n~~.~
~
STUDY OF METHODS OF ORGANIZING CALL SERVICING IN THE CONTROL COMPUTER OF.A COM-
PUT~RIZED SWITCHING CENTER
[Article by A. V. Solov'yev, Moscow , pp 138-141]
_ [Text] Efficient organization of call servicing in a control computer (EUM) can
be achieved when the operating program dispatching algorithms have the possi-
bility of flexible redistribution of its time reserves. This becomes possible
with the introduction of interrup~s, the use of static dispatching disciplines,
formed by composition of transfer rules from one queue of requests to another
and selection of queues (programs) and also with restriction of the EUM loading
in case of overloads.
The entire set of operating programs of the EUM S={sl, sNS} is divided
into groups S1, SL so that SQ n S~+ Q' = 1~ L~ k~. The
program S~ E SQ~~ = 1, NS is characterized by the order number in the
group and the group number, that is, s~ = s(i, 2), i= 1, IR, Q= 1, L.
The interaction between different groups of programs is defined using the matrix
- ?-1(t) _ ~~h~,Q~(t)~~, the elements of which h~,Q'(t) = 1 if any level program k can
interrupt the performance of any level program Q'. In cases where interruption
of the 2 level program by 2,' level programs is not permitted, the element h~,R~(t)
of the matrix H(t) is equal to zero.
Qn completion of execution of the program s(i', 2), the transition to another
program s(i", 2) is made in accordance with the following rules:
~1 on completion of servicing of each request from the queue;
A2 on detection of the control request in the queue (the control request is
placed a.t the "tail" of the queue before the beginning of servicing of the re-
quests in it);
A3 on elimination of requests in the queue.
The program s(i", 2) is selected in accordance with the rules:
gi = i" = min i, i= 1, I2
$Z - 1.~~ = y~~ lf i= S~-1~~-~ = Fk, then l~~ _~1~~ ~1~ ~ka 5~-1~
li0
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;j are the terms in the sequence ~,1, ~~_1, r,~, F,k, such that E
{1, I~}.
As a result of the composition of the rules Avl, Bv2(vl = 1, 2, 3, v2 = 1, 2)
dispatching algorithms are formed which are most frequently used when organizing
the call servicing in the EUM.
The average interrupt time of a request f~r the program s(i, Q) in the EUM for
the investigated model of organizing the call servicing is
A~, B~,
{(:,e~=(~r (~,e)tg(~,t~](!~ Rt ~
AJ,B~,. 1-Rt '
Av1Bv2
where w (i, 2) is the average waiting time for servicing of the request;
(i, 2) when using rules Avl, Bv2 in the call servicing model without interrupts,
B(i, is the average time for execution of the program 1(i, Q), RQ is the to-
tal load factor of the EUM by the programs s(i, 2) for which hQQ' = 1.
Since in a number of cases the EUM cannot provide for processing all of the in-
coming information in real time,overloads occur. The efficient organization of
the servicing of calls in the EUM in the presence of overloads is achieved when
using adaptive load limitation algorithms [1]. The algorithm for limiting the
load of the EIM which can operate jointly with any algorithm in the multilevel
model of organization of call servicing is based on using alternative operating
programs and the collective of finite automata functioning in random media.
The program si, i= l, NA is designated as al~~ernate if a request to the
EUM can be processed by any of the subroutines si (vi = 1, Nia). The
preference in processing the request by subroutine si~l decreases with an in-
crease in vi. With an increase in vi, the values of the average execution
times o� subroutines si~i decrease. The subroutine si~l is selected by the fi-
nite automaton IIi on completion of the operations fvi(vi = i, Nia). The
automaton operates in the random medium C(t) _{Ci~l(t)}. The probabilities of
penalties Ci~i(t) are ordered as follows:
~ i J r~ N a
l.~ ~t~~/ C~ (C~'~ ~C~ ~ti)� C~ ~ ~C)- CL y ~E).
The automaton Zi must ~elect the operation f~i with greatest probability during
the operating process.
The interaction of the autumaton :?i~ i= l, NA is realized in accordance
with the procedure analogous to the "common money drawer" in games of disposi-
~ tion [2]. The automaton :~i fixes the values of the overload indices Xwait and
,~flow obtained at the end of the interval Tk. The average penalty for the
player played by the automaton in one interval Tk is calculated by the formula
a = ~`.?waitXwait + �Flow,~tlow)/m~~n)
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where l3Wait~ ~fluw 3re the coefFicients selected as a function oP the composi-
tion of the alternate programs, m(Qn) is the power of the set of automata Iti
select~ng the subr~utines si~l. The automata ?titQn ~re penalized in cases where
a> ui i, where ui i is the weight of the program si i.
For investigation of the efficiency of the call servicing organization algo-
rithms in the EUM, a simulation model and program corresponding to this model
were developed. 'Itao groups of experiments were run. The call servicing organi-
_ zation model for the first group of experiments did not contain the algorithms
limiting the load of the EUM under overload conditions. The operating programs
- were dispatched on two levels: priority (reception and output of information)
and basic (information processing) with EUM loading coefficient that varips in
the range of 0.94 to 0.98. The second group of experiments was run for the same
values of the characteristics of the esternal environment of the EUM as the
first, but with organization of call servicing, an adaptive algorithm was used
for limiting the load which was based on the operation of the dispatch automata.
The simulation of the EUM program dispatch algorithms demonstrated that in the
operating range of variations of the values of the EUM load coeff icient not ex-
ceeding S percent, situations of local overloads arise. The basic level pro-
grams directly connected with the priority level of servicing the calls in the
EUM turn out to be especially unstable with respect to the local overload situ-
ations.
The adaptive EU,1 load limitation algorith~~ permit elimination of local overload
situations. The gain achieved here with respect to the values of the admissible
times the requests remain in the EUM is within the range of 18-36 percent. 'The
use of the dispatching automata made it possible to redistribute the time re-
- serves of the EiM as a function of the overload.
BIBLIOGRAPHY
l. Lazarev, V. G., and Solov'yev, A. V., "Software Elements of the EUM," PRO-
GR4~~II~VOYE UPRAVL~IIYE NA UZLAKH KOMMUTATSII [Program Control in the Switch-
ing Centers], Moscow, Nauka, 1978.
2. Varshavskiy, V. I. , KOLLIICTIViVOYE POVED~IIYE AVTOi~tATOV [Collective Behavior
of AutomataJ, Moscow, Nauka, 1973.
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- SOME METHODS OF IMPROVING THE CARRYING CAPACITY OF ~ CHr1NNEL SWITCHING NETWORK
[Article by G. L. Slepova, Moscow , pp 141-144]
[TeYt] Calls in the chanr.el switching networks (KK) can be serviced not only by
the system with rejects, but also by a combined system with rejects and waiting.
, In order to estimate the operating quality of the system with waiting, the most
important indices from the point of view of the network user were investigated:
the probability of reject p-- and the average waiting time T-- and also
the most important index from the point of view of operating efficiency of the
network its carrying capacity.
One of the reasons for using the combined servicing system (KSO) in the KK net-
works is the effort to increase the carrying capacity of the network inasmuch as
by comparison with systems with rejects, the carrying capacity and use of the
service units in the KSO are higher because the serviced load is higher.
The combined servicing system in communicatiots networks is implemented by using
limited waiting of the calls for the release of channels. Here restrictions are
imposed on the time spent by the call in the system. On the existing networks KSO with a
limited number of waiting places m-- and with a limited number of waiting
places and limited waiting time Tmax.~ have found application.
It is necessary to determine whether there is an increase in carrying capacity
of the KK network with bypasses on introduction of the KSO and the degree of
this increase. For this purpose a study was made of the nature of variation of
losses and average waiting time in the network on variation of the number of
waiting places for fixed values of the incoming flow and number of channels in
the groups. These relations were obtained by analytical calculation (1) and
they were confirmed by the statistical simulation method (2) for a fully con-
nected five-junction symmetric network wit.h a number of channels in the group
ni = n= 30 with static information distribution plan. Here it was determined
that for small incoming luads (tu a specific incoming load of K= 0.8 Erlang),
the introduction of waiting places on the service routings (channel
groups) and increasing the number of them lead to a significant decrease in the
losses for insignif~~ant values of the average waiting time comparable to the
hardware component of the call ser._uptime in the network. With an increase in
incoming load above the indicated magnitude, introduction of the KSO is not ef-
ficient, for with an increase in number of waiting places both the losses and
the average waiting time increase. This increase in losses is possible as a
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result ot nunpru~iuctive busy tim~ ot th~ ch~nnels in the waiting tia~e, tur wLtll
an increase in load, the number of waiting calls and their waiting time increase
sharply. Thus, the introduction of KSO on the KK networks without using special
control methods is efficient only for low loads and a small number of waiting
places.
In order to increase the operating efficiency of networks with KSO in the high-
load range, in the existing networks the method of limiting the nonproductive
loading as a result of waiting calls is used. This is achieved by limiting the
time spent by the call in the queue Tmax� In [2] some results from simulat-
- ing such algorithms are presented for different values of Tmax� From the point
of view of the problem stated in this paper it must be noted t:~at the applica-
tion of this method has not led to improvement of the quality indices of the
network.
Inasmuch as the investigated type of overload occurs not only as a result of
"long-waiting" calls, but also as a result of the entire mass of calls waiting
in the tandem junctions, it is expedient to use a method that is simpler to im-
plement to restrict the nonproductive load which consists in preventing waiting
- for tandem calls. In tne presence af categorizing of calls it is possible to
forbid caJ.ls of only the lowest categories from waiting. The expediency of us-
ing the ;iven method is illustrated by the method of statistical simulation in
~2)�
However, the application of the indicated method permits only partial solution
of the overload problem in a network with KSO and an increase in its carrying
capacity. As is clear from what has been investigated, when using combined ser-
vicing systems in the KK networks, the following contradictions arise. Under
conditions of low intensities of incoming flows, the use of bypasses is very.ef-
ficient, and increasing the number of waiting places reduces the network losses
ior small values of the average waiting time; for high intensities of the incom-
' ing tlows overloads and general network losses occur, and the average waiting
time increases sharply. In addition to the above-noted cause of overloads, ef-
ficient use of bypasses has significance also in a network with rejects.
In (3), the problem of finding the dynamic control algorithm which is efficient
in the entire loading range, that is, reali~es expedient distribution of the
ca11 tratfic with low load intensities and limits the load for high load inten-
sities, is solved. The "efficient" algorithm was obtained on the basis of gen-
eralizing the "efficient control" principles to the case of networks with KSO.
_ The cost of the k-th path of the j-th flow D(~~) for a system with KSO can be
selected as follows:
D(Qak) =d1 ~L)+~
~~k d' ~ ' (1)
Et~
where dl(i) the cost of the system ~I/M/nl/ml in the state i-- is estimated
as the forecasted increase in number of lost calls as a result of busy time in
Cha branch ,~1 of the channel or the waiting place; dt is the mathematical expec-
tation of the cost of the branch F E Q~, l. ~
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_ It must be noted that the cost of the path includes the instantaneous cost of
the first branch of the path and mathematical expectation of the costs of the
subsequent ones, for the expression was obtained under the assumption that the
states of the successive branches of the path, in addition to the first, is un-
known at the time of arrival of a call for which prediction takes place. This
is significant for a branch with waiting, for the call can wait in rhe process
of being set up for a random time in each tandem UK. In the case
of routing the call, a bypass path of minimum cost is selected under the condi-
tion that all the channels and a11 the waiting places are busy on the direct
path. If D(R,~) ? 1, the call is rejected. As statistical simulation has demon-
strated, as a result of the application of an efficient algorithm on a symmetric
network for m= 2 it was possible to cut the losses in the entire load range ap-
prosimately in half by comparison with the static distribution. This reduction
in losses is felt most significantly in the high-load range. This made it pos-
sible to increase the carrying capacity of the network with a specific load of
0.8 Erlang by 1 percent; with a load of 0.9 Erlang by 6 percent and with a load
of 1.0 Erlang, by 10 percent.
- It is possible to simplify the efficient algorithm. From the equality
D~~~~~'En.~,m~lYt~/E~~Yt~+ cC k d~ 3~, ~2~
~ !
~~i
where Y1 -\/u is the load intensity coming to the branch ,rl of the path 2j, un-
der the condition that the calls are distributed only with respect to the di-
rect routings, Enl~ml(Y1) is the probability that the system ~1/~1/nl/ml will be
busy; Ei(Y1) is the probability that the group of i channels will be busy for
i~ nl, for i> nl the probability that the system ~t/;1/nl/i - nl will be busy.
It is possible to find the i which satisfies condition (2). Then if on arrival
of a call on the bypass path Z~ on the branch �rl the number of servicing devices
is less than i, the call is serviced. Otherwise a reject is received. The re-
sults of simulating such a simplified algorithm demonstrated that the servicing
quality will be very close to the results obtained when using the theoretical
algorithm.
A studv was made of the dependence of the quality indices for the above-indi-
cated network on the incoming load with an increase in number or waiting places
to 10 when using the eriicient algorithm. Inasmuch as its application offers
the possibility of obtaining losses always less than when using only the forward
connectiuns, with an increase in number of waiting places and simultaneous use
ot the efficient control it is possible to obtain an increase in network carry-
ing capacity both for low and high loads. The possibility of using an efficient
algorithm combined with using the KSO to increas? the carrying capacity of the
KK network were limited only by the requirements on the maximum admissible aver-
age waiting time by a call tor beginning of servicing.
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BIBLIOGRAPHY
1. Slepova, G. L., "Approximate Method of Estimating the Servicing Quality in
Channel Switching Networks With Combined Servicing System," TRUDY UCHEBNYKH
INSTITUTOV SVYAZI [Works of the Communications Training Institutes], Lenin-
_ grad, LEIS, 1977.
2. Slepova, G. L., "Some Dynamic Teletraffic Control Algorithms in Channel
Switching Networks With Limited Waiting," AVTOMATY I UPRAVLENIYE. PRINTSIPY
POSTROYENIYA USTROYSTV RASPRIDELINIYA INFORMATSII [Automata and Control.
Structural Principles of Information Distribution Devices], Moscow, Nauka,
1978.
3. Slepova, G. L., et al., "Control Technique on Channel Switching Networks
With Bypasses and Limited Waiting," AVTOMATY I UPRAVLENIYE. UPRAVLENIYE
SETYAMI SVYAZI [Automata and Control. Communications Network Control],
~toscow, Nauka, 1979.
i
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REDISTRIBUTION OF PROBLEMS IN A MICROPROCESSOR CONTROL NETWORK WITH FAILURES
[Article by Ye. N. Turuta, Moscow , pp 145-149)
[Text] One of the prospective approaches to solving the problems of increasing
tne reliability of distributed multimicroprocessor control systems is the ap-
- proach based on ensuring the property of gradual degradation of the system in
the case of failures of its processor modules. By this property we mean the ca-
pacity of the system to reconfigure and redistribute the problems of the failed
modules among the working modules.
lfiis redistribution offers the possibility of keeping the system operating as a
whole in the case of failures of positive modules with worse, but admissible
values of some of the operating indices of the system such as output capacity,
functioning efficiency, and so on.
A study is made of a distributed multimicroprocessor technological process con-
trol system implemented in the form of a microprocessor control network (Fig-
ure 1). The functional processor modules (PM) solving the technological process
control problems realize control information and data exchange among each other
_ and with the objects of control (OU) by means of the co~nmunication network, the
junctions of which are the processor switching modules (KPM).
OU � " OU
KPM
' PM OiJ
OU
p?K OU
PM
Figure 1.
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. . .
Let us assume that PM failures are possib"le during operation of the system. The
failures of the communication network channels, KPM and objects of control are
not considered.
The state of the system at an arbitrary point in time is determined by the set
of states of its PM: r:P = Q1, Qn, where Qi E{0, 1} and Qi = 0 if the PMi
is in the f it state; Qi = 1 if PMi is in the failed state.
[Two lines missing from the original text] processes solved in the system in
the state K~; S?i ={Qi'~, Qu~, 6m~~}, i= 1, g~ is the subset of
problems solved by the working PMi in the state K~, where Qu~ 8 52~, g~ - n= kv
is the number of working PM in the siate K~, kn is the number of failed PM in
this state, _{~i, ~L~~} is the set of all technological processes (TP)
taking place in the objects of control in the state K~, v= 1, 2n - 1 inas-
much as fit PM are absent in the state ~cl = 11 1.
Organization of the redistribution of the problems of the failed PM requires ex-
ecution of the following basic steps.
1. Finding the sets S~� _{Q1~ aN}, i?i ={6~, Qu, Qmi}, 'G� _
{~1, ~�L} corresponding to the state ~c� = 00 0.
2. Determination of the correspondence between the set of all co^*_rol problems
and the set of all TP for the stat~ K�. This correspondence can be given by the
n
matrix ~~a(Ui)ki~ having R= ~ mi rows and L columns where a~ui)k = 1 if for per-
i=1
formance of the TP ~k it is necessary to solve the problem Qu and a(ui)k = 0 oth-
erwise.
3. The choice of indices on which defined requirements are imposed with organi-
zation uf redistribution of the problems.
Let us consider the case where sueh indices are the system efficiency, the out-
put capacity of the PM and the expenditures required for realizing the possibil-
ity of redistribution of the problems.
As the efficiency inde:c of the system in the state K~ let us take the value
E~ _ ~ pk, where pk is the weight of the TP ~k given by the requester.
- b kE ~p,~
We shall estimate the duration of the PMi by the mean request servicing time for
the performance of any mission su E~Zi in the PMi in the state K~.
Let us assume that the average time Ti for servicing a request in the P~ti in the
~ state K� and the matrix I~oTji~~, ,j = 1, N and i= 1, n is given, where
~T~i is the increment of the average request servicing time in the Pi~Ii on trans-
fer of the problem Q~ to it. The required e:tpenditures can be given by the ma-
- trix i~Cji~~, j= l, N and i= l, n, where C~i are the expenditures
which are required t~~ ensure the possibility of transfer of the problem aj to
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the m~dule �`!i (whzrz :j ~:'r) ~n railur~ ~i' i`~t~. L~t us as~uinr. cliac cl~~ ~�:~1~�
of C~i does not depend on in which Pr1~,othe problem Q~ is realized in the state
~c�. On transfer of the problem a~ E S2Q of the failed PMi to the working PMi two
cases are possible: [four lines missing from the original text] that the
PMi will now carry out the problem beginning not only with its own requirements,
but also the requirements of PMQ.
In case (2), transfer of problem Qu to modulus PMi involves defined expenditures
connected with the necessity for introduction of additional reserves into this
modulus. Therefore we assume that C~i = 0 if Q~ ~ Sti and C~i # 0 if Q~ ~ S2i.
- In the special case the magnitude of the expenditures Cji cannot depend on the
P?~ii to which the problem is transferred (for example, i~ all PM in the system
are the same). Then Cji = 0 if Q~ E ni and Cji = C~ if Qj ~ S2i for any i= 1,
~ qv�
Finding the set S={G~} of distributions of the problems each of which cor-
responds to the state from the given subset 1' _{!cv} of states of the system
and satisfies the requirements imposed on th~ selected indices.
'Itao approaches to organizing the redistribution of the problems in the system in
the case of P'1 failures are possible. The f.irst approach assumes that the opti-
mal distributions G~ for all states K~ 6 1' (where C is the given subset of
states) are found when designing the system and each PM is provided with the
necessary reserves to carry out the problems required both in the state K� and
in each of the states K~ E?' in accordance with the distributiQns G~ found when
building the system.
The second approach is based o~ the fact that the problem of finding the optimal
distribution G~ is solved each time (using a special decision module) for transi-
tion of the system to the state