Results of Calculations of Parameters of Reliability of Restored Devices of the Multiservice Communication Network
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| Results of Calculations of Parameters of Reliability of Restored Devices of the Multiservice Communication Network
Department of Telecommunication engineering, Tashkent University of information technologies named after Muhammad Al-Khwarizmi Tashkent city, 100084, Uzbekistan E-mail: a.muradova1982@inbox.ru
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 G , the technical utilization factor, the forced downtime factor, the operational readiness factor К O.G.. . 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. I.
Introduction 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 services. 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 multimedia services. 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. II.
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. Khalimjon Khujamatov Department of Telecommunication engineering, Tashkent University of information technologies named after Muhammad Al-Khwarizmi Tashkent city, 100084, Uzbekistan E-mail: kh.khujamatov@tuit.uz
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. III.
Problem decision 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 formula:
𝜔 ̂ (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: 𝜔 ̂ (1) =
1 20∙12
= 0,0042. 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: 𝜇 = 1
𝑣 ,
where t v – is the recovery time. In our case t v =0,13 h. Then: 𝜇 =
1 0,13
= 7,69. The time between failures is the mean time between failures. This characteristic is determined by statistical data on the failure of the formula:
𝑡̂ 𝑠𝑟
𝑡 𝑖 )/𝑛 𝑛 𝑖=1
, (2) where t i – the time of the device's good functioning between (i-1)-th and i-th failures;
In our case: t 1 = 5476 h., t 2 = 2588 h., n=1. Then by formula calculating: 𝑡̂ 𝑠𝑟
𝑡 𝑖 )/1 2 𝑖=1
= 5476+2588 1 = 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 G 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):
G
sr. /( t sr. + t v ), (3) where t
- time between failures, t v –average recovery time. In our case: К G
sr. /( t sr. + t v )= 8064 8064+0,13 = 0,999984 Statistically evaluation of the coefficient of readiness: 𝐾 ̂ 𝐺 (𝑡) = 𝑁
𝑣 (𝑡)/𝑁
0 where
𝑁 𝑣 (𝑡) - is the number of items that are in working condition at time t. The difference 𝑁 𝑣
0 - expresses the number of devices in at time t in a state of recovery (repair). In our case 𝑁
𝑣 = 19. Then: 𝐾 ̂
(𝑡) = 𝑁 𝑣 (𝑡) 𝑁 0 = 19 20 = 0,95. For the users of difficult telecommunication network’s the concept of their reliability is felt on the coefficient of readiness of the system К G , id est on attitude of time of the capable of working state of network toward time of her unplanned outage [6]. For the typical modern server of К G =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 Table 1
Coefficient of readiness, К G Maximal time of outage in a year The type of equipment 0,99
3,5 twenty-four hours Conventional 0,999 8,5 h
High reliability 0,9999
1 h Fault resilient 0,99999 5 min
Fault tolerant 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. К 𝑇𝐼 = Т 𝑠𝑟 Т 𝑠𝑟 + Т 𝑣 + Т
𝑝
where Т p – the time of outage of network, conditioned by implementation of the scheduled maintenance and repair, is counted on one refuse. К 𝑇𝐼
Т 𝑠𝑟 Т 𝑠𝑟 + Т
𝑣 + Т
𝑝 = 8064 8064 + 0,13 + 0,2 = 0,999959 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. К p = t v /( t sr. + t v ), (4) In our case: К
)=
0,13 (8064+0,13) = 0,000016. The coefficient of readiness and force downtime ratio are bound by inter se dependence.
G . (5) К p =1-К G =1- 0,999984=0,000016. A coefficient of operative readiness of К O.G.. – 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 [7].
К 𝑂.𝐺. = Т 𝑠𝑟 Т 𝑠𝑟 +𝑡 𝑣 ∙ 𝑃(𝑡
𝑥 , 𝑡) (6) where P(t
equipment of network of access on an interval (t х , t х + t) on condition that in the moment of the t х system was capable of working. For our case of P(t
К 𝑂.𝐺. = Т 𝑠𝑟 Т 𝑠𝑟 +𝑡 𝑣 ∙ 𝑃(𝑡
𝑥 , 𝑡) =
8064 8064+0,13 ∙ 0,8 = 0,799987 IV.
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 [9]: 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 completely Т sr (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 [11] 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 sr. (if ω(t)=const). 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 G . 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 dependence:
𝑃 𝐸
−𝜆∙𝑡 (7) where λ – model parameter. Frequency of refuse at an exponential model: а E (t) = -dP(t)/dt = λ∙e -λ∙t . (8) Function of intensity of refuses at an exponential model:
(t) = а E (t)/Р E (t) = λ = const. (9) Work is completely at an exponential model:
Т 𝑠𝑟.
= ∫ е −𝜆∙𝑡
∙ 𝑑𝑡 = 1/𝜆 ∞ 0 . (10) 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 [10]. 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) = (𝜆∙𝑡)
𝑛 𝑛! ∙ 𝑒 −𝜆∙𝑡 (11) 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, 6].
𝑃 𝑣 = 𝑒 −𝛼∙𝑡 𝛽 (12) 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 5 h. works without service. In case of exponential model there is intensity of refuses of equipment:
𝜆 =
𝑑𝑃/𝑑𝑡 𝑃 ≈ 10 −5 1/h.
In case of model of Weibull at β=0,5:
𝛼 = − 𝑙𝑛𝑃 𝑣 (𝑡) 𝑡 𝛽 ≈ 0,000316. Consequently, through 10 5 h. of work probability of the faultless work of equipment, forecast on an exponential model, is equal:
𝑃 𝐸 = 𝑒 −10 −5 ∙10 5 ≈ 0,37.
Prognosis on the model of Weibull: 𝑃 𝑣 = 𝑒 −0,000316∙10 2.5 ≈ 0,905. VI. Conclusion 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 Weibull model. 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. References [1] J.R. Artalejo, “G – networks: versatile approach for work removal in queuing networks”, European Journal of Operational Research,V.125, 2000, pp..233- 249.
[2] S. Chakravarthy, “The batch markovian arrival process: a review and future work”, Advances in probability theory and stochastic processes,2001, № 3. [3] G.P. Hackers, and Painters, “Big Ideas from the Computer Age”, O'Reilly Media, 2013, 276 p. [4] J.Kouns, and D.Minoli, “Information Technology Risk Management in Enterprise Environments: A Review of Industry Practices and a Practical Guide to Risk Management Teams”, 2013, 421 p. [5] W.Mao, and P.Hall, “Modern Cryptography: Theory & Practice”, Professional Technical Reference, New Jersey, 2004, 308 p. [6] A.Tomlinson, “Introduction to the TPM”, Smart Cards, Tokens, Security and Applications, Springer, 2012, pp.155 -172. [7] R. E.Barlow, and F.Proschan, “Mathematical theory of reliability”, SIAM, 1996. [8] K. A. Harras, M. P.Wittie, K. C.Almeroth, and M. E. Belding, “ParaNets: A Parallel Network Architecture for Challenged Networks”, in Proc. of the 7th IEEE Workshop on Mobile Computing Systems and Applications (Hotmobile), Tucson, AZ, pp.73-78, February, 2007. [9] T.Nishanbayev, and A.Muradova, “The system research of reliability indexes of modern infocommunication networks with distributed structure with the workload of its components”, The advanced science journal, USA, 2014, pp.59-64. [10] A. Muradova, “Calculation in the NGN networks of indexes of reliability of tracts of transmission of packet information”, The advanced science journal, USA, 2014, pp.24-28. [11] Rakhimov, B.N., Rakhimov, T.G., Berdiyev, A.A., Ulmaskhujayev, Z.A, Zokhidova, G. “Synchronous data processing in multi-channel information measuring systems of radiomonitoring”,An International Journal of Advanced Computer Technology. Compusoft,, 8(3),2019,pp. 3088-3091 . Download 106.98 Kb. Do'stlaringiz bilan baham: 
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