=Paper=
{{Paper
|id=Vol-2341/paper-02
|storemode=property
|title=Generalized Model of Functioning of Generator Equipment of Synchronization Network With The Limited Reliability of its Elements
|pdfUrl=https://ceur-ws.org/Vol-2341/paper-02.pdf
|volume=Vol-2341
|authors=Andrew K. Kanaev,Andrew A. Privalov,Valery V. Sapozhnikov,Eugene V. Oparin
}}
==Generalized Model of Functioning of Generator Equipment of Synchronization Network With The Limited Reliability of its Elements==
https://ceur-ws.org/Vol-2341/paper-02.pdf
Generalized Model of Functioning of Generator Equipment of
Synchronization Network with the Limited Reliability of its
Elements
Andrew K. Kanaev Andrew A. Privalov
Department of Electrical Communication, Department of Electrical Communication,
Emperor Alexander I St. Petersburg State Emperor Alexander I St. Petersburg State
Transport University Transport University
Saint Petersburg, Russia Saint Petersburg, Russia
kanaevak@mail.ru aprivalov@inbox.ru
Valery V. Sapozhnikov Eugene V. Oparin
Department of Autom. Remote Control, Communication department,
Emperor Alexander I St. Petersburg State “Giprotranssignalsvyaz” - branch of JSC
Transport University “Roszheldorproekt”
Saint Petersburg, Russia Saint Petersburg, Russia
TrES-4b@yandex.ru onapuh@mail.ru
The main purpose of the synchronization network is
to maintain the coordinated interaction of the digital
communications equipment of the
Abstract telecommunications system. This coordinated
interaction is ensured by the generation,
In the given article the estimation of transmission and delivery of the synchronization
stationary characteristics of reliability of the signals necessary to provide and maintain
generator equipment of telecommunication synchronous operation of the TCS equipment
system (TCS) with use semi-Markov models [Dav04].
is resulted. A generalized semi-Markov The occurrence of failures in the synchronization
model of the process of functioning of network and the deviation of the quantitative and
generator equipment is proposed, with the qualitative characteristics of the clock signals can
separation of states reflecting the main cause a significant deterioration in the quality of the
operating modes of the TCS generator transmitted data, up to the total refusal to provide
equipment. Based on the developed semi- telecommunications services. Given this feature of
Markov model, the stationary reliability the synchronization network, an important role is
characteristics of the generator equipment played by the process of ensuring a given
are calculated, which reflect its integral reliabilityof its elements, as well as solving
state. problems of evaluation and prediction of reliability.
An important role is played by the process of
1 Introduction managing the synchronization network as an integral
part of the TCS, ensuring the required performance
Modern information systems taking into account the of its operation. Particularly relevant are the issues
applied information technologies in their work are of managing the synchronization network during
based on telecommunication systems (TCS). One of periods of failure, including as a result of external
the key TCS subsystems that support its operation is influences. In these states, it is necessary to restore
the synchronization network.1 the functioning of the synchronization network
within a given time to ensure the stability of the
entire TCS. In the process of managing the
Copyright © by the papers’ authors. Copying synchronization network, an important task is not
permitted for private and academic purposes. only to evaluate the current generator equipment and
In: B. V. Sokolov, A. D. Khomonenko, A. A.
Bliudov (eds.): Selected Papers of the Workshop
Computer Science and Engineering in the and Natural-Scientific Training in Engineering
framework of the 5 th International Scientific- Education", St.-Petersburg, Russia, 8–9 November,
Methodical Conference "Problems of Mathematical 2018, published at http://ceur-ws.org
6
other elements of the synchronization network, but small-scale networks, it is sometimes permissible to
also to forecast the states and reliability indicators in use separate PRSs in conjunction with a secondary
order to prevent failures and emergencies. master oscillator (SMO).
There is a complex of methods for assessing the The primary reference generator is a complex of
reliability of the elements of the TCS and the equipment containing three PEI and SMO. As a rule,
process of functioning of the TCS, among which a PRG is the main source of reference clock signals on
special place is occupied by semi-Markov methods the synchronization network. The equipment that is
for assessing reliability. The advantage of using part of the PRG can be completely autonomous and
semi-Markov methods of reliability evaluation is the use only cesium or hydrogen PRS. The PRG output
ability to produce simulations in cases where the law signals should not change their duration for any
of distribution of the occurrence of failures differs switching in the equipment by more than 1/8 of the
from the exponential distribution law. Semi-Markov clock interval.
models are also used in cases where there is an The output signals of PRG equipment are usually
independence of the probabilities of a transition the 2.048 MHz and 2.048 Mbit/s clock signals, as
from one state of the process of functioning to well as other reference signals, the need for which
another from previous transitions between states, may appear when the digital network is
and also when the law of distribution of the synchronized (64, 100 kHz, 1, 5 and 10 MHz).
residence time in states does not depend on previous The main characteristics of the PRS are regulated
stages of functioning [Shu12, Ush85]. In view of the and outlined in ITU-T Rec. G.811 [ITU98/1].
foregoing, in most cases, the processes of the To restore and maintain the necessary quality of
functioning of the subsystems of the TCS can be sync signals on the synchronization network, there
considered as semi-Markovian, for which it is are the SMO and the local master oscillator (LMO).
possible to estimate and predict the reliability Due to the fact that the LMO have slightly worse
indicators. characteristics than the SMO, they are applied only
on the sections of the synchronization network, from
2 Types Of Generating Equipment Used which the synchronization signals do not flow to
In Telecommunication System other LMO or SMO. To ensure reliable
synchronization, the synchronization network of
Synchronization Networks almost any telecoms operator should be based on
As sources of synchronization signals on digital own equipment of the SMO or LMO.
communication networks, primary reference sources In many cases, the SMO is additionally connected
(PRS) are used, the characteristics of which are with the PRS in order to more reliably reserve the
governed by international Recommendations reference clock signals. Thus, the SMO and the
[ITU98/1, ETS98/1]. The performance requirements LMO are widely used on the digital network and are
determine the permissible long-term deviations of the main element of the synchronization network.
the PRS frequency from their nominal value, the Availability on the network of equipment of the
limiting values of the wanderings of the output SMO and LMO allows to organize the system of
signals, expressed in terms of the maximum time control and monitoring of the synchronization
interval error (MTIE), deviation of the time interval network and, to some extent, to provide control over
(DTI), and permissible changes in the duration of the state of the entire digital network. The technical
the clock interval with all possible internal requirements for the SMO and the LMO are defined
switching. In accordance with the Recommendations in ITU-T G.812 [ITU98/2].
for PRS output signals, "the maximum permissible The SMO provides the choice of the best
frequency deviation from the nominal value should synchronization input from a number of sources,
not exceed for all practicable environmental while ensuring the necessary processing and
conditions and observation times of not less than filtering of the clock signals, with their subsequent
one week". On the synchronization networks, distribution. In the event of failure of all input
various types of PRS can be used, both forming the interfaces, loss of all input signals or degradation of
sync signals independently, and using reference their characteristics to a level below the required
clock signals transmitted by other systems not values, the LMO should memorize the frequency of
directly connected to communication systems. As switching to the frequency memorization mode in
PRS, creating a sync signal for communication accordance with ETS 300 462-4 and ITU-T Rec.
systems, can serve as cesium or hydrogen ITU-T G.812 [ITU98/2, ETS98/2]. The secondary
generators. Reference synchronization signals can master oscillator is synchronized with external
also be obtained by signal receivers transmitting synchronization signals of 2048 kHz or 2048 kbit/s.
earth stations operating on long waves or signals The number of output interfaces of synchronization
from satellite navigation systems. To synchronize signals with a frequency of 2048 kHz in the
communication networks, not individual PEIs are composition of the SMO is usually not less than 12
used, but a complex consisting of several PEIs, with the possibility of increasing to 64, and the
called the primary reference generator (PRG). In
7
number of output interfaces of synchronization process of operation of the generator equipment
signals of 2048 kbit/s is at least two. necessarily includes the following states:
The SMO also includes a synchronization signal s1 – power supply of generator equipment;
converter, which restores the original clock s2 – initialization of the software, warming up
characteristics in information signals of 2048 Kbit/s and self-testing of the generator equipment;
that have come to this node using the plesiochronous s3 – setting the mode of free oscillations with the
digital hierarchy (PDH) systems or extracted from selection of the external synchronization signal;
the systems of the synchronous digital hierarchy s4 – setting the mode of synchronous operation
(SDH). This signal, denoted as E1/T, can later be with accumulation of memory for the hold mode;
used to synchronize the equipment. For monitoring s5 – setting the hold mode;
and for frequency comparison, the SMO consists of s6 – failure of generator equipment and
1/5 MHz output interfaces. subsequent restoration of its operability.
Local master generators are used on local network The operation of the generator equipment is as
sites as the last reference for synchronization. The follows. The initial state is the state s1. After turning
local master oscillator is intended for use on on the power supply of the generator equipment, the
synchronization nodes and small-scale network initialization mode starts, software checks with
sections that do not contain the SMO, for the simultaneous heating of the element and self-testing.
reconstruction and multiplication of clock signals Further, the generator equipment enters the free
arriving via communication lines from PRG or oscillation mode with analysis and selection of the
SMO. The structure of the LMO is similar to the external synchronization signal.
structure of the SMO, with the difference that the
LMO allows the use of simpler master oscillators,
which to a lesser extent suppress phase noise and
have a less accurate mode of frequency
memorization.
The lowest link in the hierarchy of generator
equipment is the generator of the network element
(GNE) is a master generator built into the network
element (multiplexer), which receives
synchronization inputs from a number of external Figure 1: Semi-Markov model of the generator
sources, selecting one of them and producing the equipment operation process
minimum filtering. In the event of damage to all
input reference synchronization signals in the GNE, The mode of free oscillations is characterized by the
an internal self-master oscillator shall be used fact that in this mode of operation there is no control
which, in the frequency memorizing mode, will over the frequency of the internal oscillator. This
store approximately the frequency of the input clock mode of operation occurs after the initialization of
in accordance with ETS 300 462-5 and Rec. ITU-T the software of the generator equipment, when
G.813 [5, 8]. external clock signals are not used, and also when
To the master generator of the network element, faults occur in the synchronization circuits. In this
according to the recommendation G.813, case, the quality of the external sync signals
requirements are imposed for the permissible becomes inadmissible for use, and there is not
relative error of the natural frequency, which should enough data in the generator to go into hold mode.
not exceed 4.6·10-6 and the presence of a storage When the external synchronization signal is
mode, the error of frequency memorization with loss selected, the equipment of the synchronization
of the synchronization signal should be no more network starts to gradually enter the synchronous
than 5.0·10-8, and the daily frequency drift is less operation with external clock monitoring. The
than 1·10-8. synchronous operation mode is the main mode of
operation of the generator equipment. In this mode,
3 Semi-Markov Model Of The Process the signal at the output of the generator equipment is
Of Functioning Of The Generator monitored with an adjustable phase-locked loop
with an allowable accuracy of the signal change at
Equipment the input of the external synchronization. At the
To assess the stationary reliability characteristics of same time, the necessary data is accumulated to
generating equipment in the TCS, it is necessary to ensure the required accuracy of the signal in the hold
form a model of the process of its functioning. This mode. If there is an external sync signal and
model is formed (Figure 1) and reflects all the basic accumulation of memory, the generator equipment is
modes of operation of generator equipment. Despite completely switched to the synchronous operation
the great variety of types and versions of mode. In this mode of operation, if the quality of the
synchronization equipment, clock generators and sync signals deteriorates or their loss disappears, the
equipment for their distribution, the model of the generator equipment goes into a hold mode, and it is
8
possible to go back to the synchronous operation equipment in each state, we use the following
mode in case of restoration of the required quality of expressions [Shu12] (2, 3):
clock signals and storage of memory. The hold Ti pij Tij
mode occurs after working in synchronization mode jS
as a result of faults in the synchronization circuits. (2)
In this mode, the signal at the output of the generator
equipment does not depend on the signal at the Tij (t ) [1 Fij (t )]dt
input, but is determined by the values of the control 0 (3)
signal from the device memory, as well as the where Tij is the mathematical expectation of the
accuracy of storing the control signals, processing conventional time of the generator equipment in
the stored signal values, and frequency deviations of each state.
the generator due to the influence of destabilizing To estimate the stationary probability of an
factors. embedded homogeneous Markov chain in the state
The hold mode only occurs if the generator si, we use the following expression [Shu12] (4, 5):
equipment was in the synchronous operation mode
for a long time until the failure, and at the same time Di
enough data was accumulated to ensure the required Pi n
initial synchronization signal accuracy in the hold
mode. D j 1
j
The transition between the operation modes of the (4)
generator equipment can be carried out in a directive where Di (Dj) is the minor obtained by deleting i(j)
way by sending the appropriate commands from the of the row and i(j) of the column of the matrix D.
operating personnel. It is believed that the 1 p11 p12 ... p1n
occurrence of a refusal can occur at any time.
p 21 1 p 22 ... p 2 n
D
4 Determination Of Reliability Indicators
... ... ... ...
Of Generator Equipment On The Basis p
n1 p n2 ... 1 p nn
(5)
Of The Developed Semi-Markov Model
To estimate the mean time between failures T 0 and
Of The Process Of Its Functioning average downtime TПР, the final set of states S of the
The main stationary characteristics of the reliability process of generating equipment operation is
of the generator equipment will be: divided into two disjoint subsets of workable states
Stationary probabilities i , i 1,...,6;i S
of the S P S and inoperable states S P S , where
generator equipment staying at an arbitrary time in
SP SP 0 .
each of the states si;
Mean time between failures T0 and average idle S P will be the states s1, s2, s3, s4
The effective states
time of generator equipment TПР.
The initial data for evaluating the reliability of S
and s5. An inoperable state P is the state s6.
generator equipment are [2]: In the presence of the specified initial data, the mean
П (p ) time between failures of the system and the average
- The matrix of transition probabilities ij
;
idle time can be found from the following
- The matrix of the distribution functions of the
expressions [2]:
conditioned random times of the generator
equipment in each of the si states Fij(t); PT i i
The stationary probability of the generator iS P
T0
equipment staying at an arbitrary moment of time in
each of the states si can be calculated by the
P p
iS
i ij
jS P
following formula [2]: (6)
i
Pi Ti
(i, j 1,...,6; i, j S ; i 1) PT i i
Pj T j iS TПР
iS P
jS
(1) P p i ij
where, Pi, Pj is the stationary probability of the stay iS _ jS P
(7)
of the embedded homogeneous Markov chain in the
state si and sj, Ti, Tj is the mathematical expectation S S
where and _ is the subset of the boundary
of the unconditional residence time of the generator operable and inoperative states that condition the
equipment in each state, S is the total number of S P to a subset S P and vice
states. transition from a subset
To estimate the mathematical expectation of the versa.
unconditional residence time of the generator
9
0 0.2 0 0 0 0
A subset of the boundary states S is the states s2,
S_ 0 0 0.25 0 0 0.25
s3, s4, s5. The subset of the boundary states is 0 0 0 100 0 0.33
the state s6. Tij
0 0 100 0 1000 0.5
Estimating the stationary probabilities i of the 0 0 100 1000 0 0.5
generator equipment at any time in each of the states 0.2 0 0 , h (12)
0 0 0
si, it is possible to determine the availability and idle
factors according to the following expressions The mathematical expectations of the unconditional
[Shu12, Sta10]: residence times of the generator equipment in each
state will take the following form (13):
К Г i
Ti (0.2 0.25 95.017 495.05 905.025 0.2) , h (13)
iS P
(8) The stationary probabilities of the stay of the
К ПР i 1 К Г embedded homogeneous Markov chain in the states
iS P
(9) si take the following form (14):
Pi (0.061 0.061 0.235 0.376 0.207 0.061) (14)
Thus, the following steady-state probabilities of the
generator equipment stay at an arbitrary instant of
5 Calculation of numerical values of time in each of the states si (15):
stationary reliability characteristics of 1 3.077 10 5 ;
generator equipment 2 3.846 10 4 ;
As an example, an estimate of reliability indicators 3 0.057 ;
of the generator equipment of the
telecommunications operator is given below. The 4 0.47 ;
following data are accepted as initial data. The 5 0.473 ;
matrix of transition probabilities has the following
form (10): 6 3.077 10 5 .
0 1 0 0 0 0 The probability data i show that at any random
0 0 0.95 0 0 0.05 time the generator equipment is in one of the states
0 0 0 0.95 0 0.05 si.
П Mean time between failures T0 and average idle time
0 0 0.45 0 0.45 0.1
0 TПР of generator equipment will be calculated as
0 0.05 0.9 0 0.05 follows (15, 16):
1 0 PT
0 0 0 0 (10) iS PPT P T P T P T P T
i i (15)
T0 2418 h
1 1 2 2 3 3 4 4 5 5
As the distribution of the conditioned random time P p (P p P p P p P p )
iS
i
jS P
ij 2 26 3 36 4 46 5 56
of the generator equipment in each of the si states
Fij (t ) , an exponential distribution is adopted with PT i i
P6T6 (16)
iS P
TПР 0.684 h
the following transition intensities matrix (11): P p
iS _
i
jS P
ij P6 p 61
0 5 0 0 0 0 Accordingly, the availability factor and idle ratio
0 0 4 0 0 4 will take the following values (17, 18):
0 3 0.99996923 (17)
0 0 0.01 0
К Г
i S P
i 1 2 3 4 5
0 0 0.01 0 0.001 2
0 К ПР i 1 К Г 3.077 10 5 (18)
0 0.01 0.001 0 2 iS P
5 0 , h Similarly, based on the developed model of the
0 0 0 0 (11)
process of generating equipment operation,
Thus, after the subsequent calculation based on the
reliability indicators of any synchronization
proposed approach and the developed model of the
equipment can be used.
process of the generator equipment operation, the
following results were obtained. The matrix of
mathematical expectations of the conventional times 6 Conclusion
of the generator equipment in each state will take the The synchronization network is an important
following form (12): subsystem of TCS, which directly affects the quality
of providing communication services. To timely
prevent failures in the synchronization network, a
10
sound evaluation of the reliability of the [Ush85] Reliability of technical systems: Reference
synchronization equipment is required, with the help book. Ed. I.A. Ushakova / Yu. K.
of which the maintenance personnel can Belyaev, V.A. Bogatyrev, V.V. Bolotin
preventively perform replacement and repair. In this and others. - M.: Radio and
connection, this article presents the results of Communication, 1985. – p. 608.
estimating stationary reliability characteristics of [ITU98/1] Time characteristics at the outputs of
generator equipment using semi-Markov models. primary reference reference generators:
The obtained results will allow to estimate the ITU-T Recommendation G.811. - 1998.
reliability indicators on the basis of the statistics of
the technical operation of the synchronization [ETS98/1] Transmission and multiplexing (TM):
network equipment, and, consequently, to conclude General requirements for synchronization
that it is advisable to continue using a separate type networks. Part 5. Time characteristics of
of equipment or replace it for further repair. It is slave generators for operation in the
assumed that the distribution functions of the equipment of the synchronous digital
conditional random time of the synchronization hierarchy SDH: European
network element in each of the states will be Telecommunication Standard ETS 300
determined from the practice of operating the 462-5. - 1998.
synchronization network, which will allow to obtain
a model of the process of functioning of the [ITU98/2] Temporary requirements for slave master
generator equipment with real properties. This generators suitable for use as nodal in
model is universal, differs from the completeness of synchronization networks: ITU-T
the state registration and can be applied to any kind Recommendation G.812. - 1998.
of generator equipment, and also allows to
determine the probabilistic and temporal [ETS98/2] Transmission and multiplexing (TM):
characteristics of each state of the generator General requirements for synchronization
equipment under study, which allows, when networks. Part 4. Time response driven
imposing regulatory requirements on the generators to ensure synchronization of
probability-time characteristics, to formulate a set of synchronous digital hierarchy equipment
strategies for achieving them through control (SDH) and plesiochronous digital
probability-time characteristics of individual states. hierarchy (PDH): the European
telecommunications standard ETS 300
References 462-4. - 1998.
[Dav04] Clock network synchronization / P.N. [ITU98/3] Timing characteristics of SDH master slave
Davydkin, M.N. Koltunov, A.V. Ryzhkov generators: ITU-T Recommendation
- M.: Eko-Trends, 2004. – p. 205. G.813. - 1998.
[Shu12] Structural reliability of information systems. [Sta10] GOST R 53480-2009 reliability in the art.
Methods of analysis / I.B. Shubinsky. - Terms and Definitions. - Moscow:
Ulyanovsk: Regional Printing House Standartinform, 2010. – p. 33.
"Printing Yard", 2012. – p. 216.
11