Results of Calculations of Parameters of Reliability of Restored Devices of the Multiservice Communication Network
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- Abstract: In the article made the calculation of the statistical
Results of Calculations of Parameters of
Reliability of Restored Devices of the Multiservice
Department of Telecommunication engineering,
Tashkent University of information technologies named after
Tashkent city, 100084, Uzbekistan
evaluation of the coefficient of readiness and the results of the
calculation. The definition of a multiservice communication network is
given, the purpose of each level of the network and their main
equipment are given. The main reliability indicators devices of access
layer are presented and calculated, such as: the failure flow parameter,
the time between failures, the availability factor К
, the technical
utilization factor, the forced downtime factor, the operational readiness
. Brief recommendations on the choice of methodology for
calculating reliability indicators of telecommunications network
equipment are given.
keywords: multiservice communication network, access level,
management level, quality of service, agreement on the level (quality)
of providing network services, recoverable devices, quantitative
characteristics, failure probability, recovery time, recovery rate, failure
flow, availability factor, time to failure, operational availability.
Multiservice network is a network of communication
constructed in accordance with the concept of a new generation
communication network and providing an unlimited range of
A multiservice network is a single telecommunications
structure capable of transmitting heterogeneous information
(voice, video, data) at a speed exceeding tens of thousands of
existing data rates (literally, a multi-service network is a network
in which more than one service is provided). This approach is
based on the integration of all users into a single broadband
network that provides various types of services - high-speed
Internet access, video data (for example, data from street video
cameras), television, IP telephony, home networking and various
The main advantages of using multiservice networks is the
ability to reduce, reallocate the cost of implementing and
maintaining telephony and data services by varying the bandwidth
of communication channels and the ability to support complex,
resource-intensive multimedia applications that extend the
functionality of network equipment.
Statement of a problem
Architecturally, the structure of a multiservice network can be
divided into several main levels: the backbone, the level of
distribution and aggregation, and the level of access.
Department of Telecommunication engineering,
Tashkent University of information technologies named after
Tashkent city, 100084, Uzbekistan
The backbone level is a universal high-speed and, as far as
possible, uniform information transfer platform, implemented on
the basis of digital telecommunication channels. The distribution
level includes the network equipment of the operator's network,
and the aggregation level performs the tasks of aggregating traffic
from the access level and connecting to the backbone (transport)
network. The access level includes corporate or intra-house
networks, as well as communication channels, providing their
connection to the node (nodes) of the distribution network.
To the equipment of multiservice communication networks
include gateways, access switches, routers, soft switches, servers,
services and other devices based on packet switching.
The basic concepts for multiservice networks are QoS
(Quality of Service) and SLA (Service Level Agreement), i.e.
quality of service and agreement on the level (quality) of the
provision of network services. The transition to new multiservice
technologies changes the very concept of service delivery, where
quality is guaranteed not only at the level of contractual
agreements with the service provider and the requirements for
compliance with standards, but also at the level of technologies
and operator networks.
Since the quality of service is directly related to the reliability
of the network, so it is necessary to calculate the reliability of the
equipment of each level and the network as a whole.
Restoring call such network devices, which in the exercise of
his functions to allow for the repair. If there is a failure of such
equipment, it will cause cessation of operation of the equipment
only for the period of elimination of failure. These devices
include: switches, routers, software switches, various service
servers, remote hubs, PBX. Non-recoverable devices do not allow
repair during the performance of their functions. If such
equipment fails, the operation to be performed will be disrupted
and must be started again if a failure can be resolved. These
devices include equipment as a single action (Board circuits,
circuit Board racks PBX, electronic elements), and the device of
multiple actions (some systems management software stations,
responsible manufacturing processes, etc.).
Recoverable devices of access level of multiservice
communication network include: gateways, access switches,
remote concentrators, PBX, DSLAM equipment. In the operation
of the network when restoring the device, thanks to the flexibility
of its work and the possibility of replacing in case of emergency,
allow you to decrease the level of security to the entire network
as a whole. Therefore, the actual solution of the problem of
calculating the main reliability indicators of the network devices
to be installed, as well as the equipment of each level of the
multiservice communication network.
III. Calculation of Parameters of Reliability
Reliability indicators of recoverable devices can include: for
example, the failure flow parameter, the time between failures, the
availability factor, the forced idle rate, the recovery rate [1, 2, 3].
The parameter of the failure flow is the ratio of the number of
failed devices per unit of time to the number of tested objects,
provided that all the failed elements are replaced with serviceable
ones (new or repaired).
Statistically, this indicator is estimated using the following
̂ (𝑡) = 𝑛(∆𝑡)/(𝑁 ∙ ∆𝑡), (1)
where n(∆t) - is the number of failed elements in the time
interval from t-∆t/2 to t+∆t/2; N – is the number of elements
tested; ∆t is the time interval.
In our case, the access level equipment is being investigated,
namely the operation of gateways. Here n=1 is the number of
failed elements in the time interval (for the time ∆t is the time
interval from 1 to 12 months), N=20 is the number of test
elements. Then, according to the formula, we calculate:
̂ (1) =
For any time point, regardless of the law of distribution of
uptime, the failure flow parameter is greater than the failure rate,
i.e. ω(t)>а(t). The intensity of recovery is estimated:
– is the recovery time. In our case t
=0,13 h. Then:
The time between failures is the mean time between failures.
This characteristic is determined by statistical data on the failure
of the formula:
– the time of the device's good functioning between
(i-1)-th and i-th failures;
In our case: t
= 5476 h., t
= 2588 h., n=1. Then by formula
= 8064 ℎ.
MTBF (meal time between failures) is a characteristic of
reliability, which is widely used in practice. The parameter of the
failure flow and the time between failures characterize the
reliability of the repaired element and does not take into account
the time required for its restoration. Therefore, they do not
characterize the readiness of the element to perform its functions
at the right time. For this purpose, such criteria as the availability
factor and the forced downtime factor are introduced. The
availability factor К
is used as an indicator of reliability, if in
addition to the fact of failure it is necessary to take into account
the recovery time. The availability factor is defined as the
probability that at any given time t the element is in a state of
operability (except for planned periods during which the
application of the elements is not foreseen):
- time between failures, t
–average recovery time.
In our case: К
Statistically evaluation of the coefficient of readiness:
(𝑡) = 𝑁
(𝑡) - is the number of items that are in working
condition at time t.
- expresses the number of devices in
at time t in a state of recovery (repair). In our case
= 19. Then:
For the users of difficult telecommunication network’s the
concept of their reliability is felt on the coefficient of readiness of
the system К
, id est on attitude of time of the capable of working
state of network toward time of her unplanned outage . For the
typical modern server of К
=0,99, that means an approximately
3,5 twenty-four hours of outage in a year. Classification of
equipment on the level of reliability, shown in a table 1.
Classification of equipment on the level of reliability
Coefficient of readiness,
Maximal time of outage in a
The type of
3,5 twenty-four hours
A coefficient of the technical use is a relation of the expected
value of time of stay of network domains as systems in the capable
of working state for some period of exploitation to the sum of the
expected values of time of stay of network domains in the capable
of working state, outages, conditioned by technical service, and
repairs for the same period of exploitation.
– the time of outage of network, conditioned by
implementation of the scheduled maintenance and repair, is
counted on one refuse.
8064 + 0,13 + 0,2
A force downtime ratio is name the relation of time of renewal
to the sum of times of work on a refuse and time of renewal taken
for the same calendar term.
In our case: К
The coefficient of readiness and force downtime ratio are
bound by inter se dependence.
A coefficient of operative readiness of К
– is probability
that a device will appear in the capable of working state in
arbitrary moment of time, except the planned periods during that
application of device on purpose is not envisaged, and, since this
moment, will work smoothly during the set time domain .
, 𝑡) (6)
equipment of network of access on an interval (t
+ t) on
condition that in the moment of the t
system was capable of
working. For our case of P(t
, 𝑡) =
∙ 0,8 = 0,799987
Choice of reliability indexes
Reliability indexes in every case must be chosen so that they
by the best character characterized reliability of device on his
having a special purpose setting. There are the special
methodologies on the choice of reliability of equipment of
telecommunication network’s indexes, we will bring some short
recommendations over :
1. If an unrefurbishable device works singly during the small
set span of time t
, that as a reliability index it is expedient
to choose probability of faultless work of Р(t
) for the set time.
2. If the refuse of unrefurbishable device does not entail hazard
effects and a device is exploited to the offensive of refuse, then it
is expedient to characterize his reliability through middle work
(electro mechanics devices).
3. If an unrefurbish able device is characterized constancy of
intensity of refuses, then as reliability it is expedient to use her
value λ. This index is used for description of unrefurbish able
electronic knots (IS and BIS).
4. If time of renewal of refurbish able device is small as
compared to time of faultless work it is expedient to use reliability
indexes ω(t) and t
, when ω(t)=const.
For the responsible managers of the technical systems  the
refuse of that entails heavy consequences, in spite of speed of
renewal, it is expedient to use as a reliability index the parameter
of stream of refuses ω(t) or work on the refuse of t
5. If a substantial value has an available time of work of
refurbish able device, as a reliability index it is expedient to use
the coefficient of readiness of К
. This index is used for universal
telecommunication networks, where a substantial value is had loss
of machine time.
6. If faultless work has an important value in periods of
implementation of operation, then how a reliability index is used
coefficient of operative readiness.
From the expressions considered higher for the estimation of
quantitative descriptions of reliability evidently, that all
descriptions, except a mean-time-to-failure are the functions of
time. Time between nearby refuses for the elements of apparatus
is a continuous casual size that is characterized some law of
distribution. Dependence of reliability on time is described by
means of mathematical model of reliability (ММR) -
mathematical expression (formula, algorithm, equalization,
system of equalizations) allowing to define reliability indexes.
Simplest ММR as formulas carry the name of statistical models
of distribution. At research of reliability the next models of
distribution are used: exponential, normal, Relay, Poisson,
Weibull of and other [1, 2, 3, 6].
The most widespread statistical model of reliability is an
probability of faultless work of device is expressed by
where λ – model parameter.
Frequency of refuse at an exponential model:
(t) = -dP(t)/dt = λ∙e
Function of intensity of refuses at an exponential model:
(t) = а
(t) = λ = const. (9)
Work is completely at an exponential model:
= ∫ е
∙ 𝑑𝑡 = 1/𝜆
An exponential model can be used in the case when intensity
of refuses permanent size (λ=const), and also as description
suffices difficult refurbish able objects in the period of
exploitation, if to eliminate the period of earning extra money and
period of the intensive aging.
To the exponential model the model of Poisson is closely
related. She is based on an idea about the stream of random events,
called Poisson’s, if executed condition of stationarity,
ordinariness and absence of after action .
A stationarity is the property of stream, expressed in that the
parameters of stream do not depend on time.
Ordinariness is the property of stream, expressed in that one
event can happen in the same moment of time only.
Absence of after action is the property of stream, expressed in
that probability of offensive of this event does not depend on that,
when previous events happened and how many of them were.
V. Result and Discussion
Thus the model of Poisson allows to express probability of Р(t,
n) that on the set time domain happened equal n events (refuses),
if time between separate events (by refuses) is up-diffused
exponentially with a parameter λ. On the model of Poisson:
𝑃(𝑡, 𝑛) =
The model of Weibull finds practical application due to the
simplicity and flexibility, because depending on the values of
parameters model character mutates in wide limits. The model of
reliability of Weibull, named also the model of Weibull -
Gnedenko, offered the Swedish scientist. Weibull as a model of
durability of materials, and then reasonable mathematically the
Russian scientist B.V. Gnedenko. Probability of faultless work on
the model of reliability of Weibull is expressed by a formula [1,
where α and β – parameters of model.
Approximately value β=0,2÷0,4 for electronic devices with
the decreasing function of intensity of refuses.
Let probability of faultless work of equipment after t=1000 h.
Р=0,99 is equal, we will make the prognosis of probability of
faultless work of the same equipment through 10
without service. In case of exponential model there is intensity of
refuses of equipment:
In case of model of Weibull at β=0,5:
𝛼 = −
Consequently, through 10
h. of work probability of the
faultless work of equipment, forecast on an exponential model, is
Prognosis on the model of Weibull:
Calculations have shown that the choice of the correct
reliability model determines the calculation of reliability
indicators and the results of the multiservice network access
equipment. Normal distribution and the Rayleigh model we use to
describe such networks and devices that are exposed to wear, here
the value of intensity λ(t) monotonically increases. The choice of
reliability model is a complex scientific and technical problem. It
can be satisfactorily solved by standard methods of mathematical
statistics, if there is a large statistical material about failures of the
studied devices. Because of the high reliability of the equipment
and its components, there is usually little statistical data on
failures. In the latter case, when choosing a model, we use the
results of accelerated tests carried out under heavy equipment
conditions, physical considerations, previous experience. In the
case of approximate estimates, we choose the exponential model
as the most convenient from the point of view of analytical
transformations. The exponential model is recommended to use in
the calculations of reliability in the absence of other input data for
calculation, except for the failure rate. If you have more complete
source data, use a different, more accurate model, such as the
In further studies, indicators of reliability of transport
equipment and management level of multiservice communication
network will be calculated. After calculating the reliability of the
equipment of each level of multiservice communication network,
all the results will be merged into one system and presented in the
form of a mathematical model using a systematic approach.
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