Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation

The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probabi...

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Autores principales:	Sergey Stepanov, Mikhail Stepanov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	emergency services performance evaluation repeated calls Markov process system of state equations recursive algorithms Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/4da7ad8108274e19969bcf2435a4a4b2
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id	oai:doaj.org-article:4da7ad8108274e19969bcf2435a4a4b2
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spelling	oai:doaj.org-article:4da7ad8108274e19969bcf2435a4a4b22021-11-11T18:20:38ZEstimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation10.3390/math92128112227-7390https://doaj.org/article/4da7ad8108274e19969bcf2435a4a4b22021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2811https://doaj.org/toc/2227-7390The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probability that a customer repeats the call. Such models are seen in the modeling of various telecommunication systems such as emergency information services, call and contact centers, access nodes, etc., functioning in overloading situations. The stationary behavior of the system is described by the infinite-state Markov process. It is shown that stationary characteristics of the model can be calculated with the help of an auxiliary model of the same class but without call repetitions due to losses occurring before and after the occupation of a free server and the aging of transmitted information. The performance measurements of the auxiliary model are calculated by solving a system of state equations using a recursive algorithm based on the concept of the truncation of the used state space. This approach allows significant savings of computer resources to be made by ignoring highly unlikely states in the process of calculation. The error caused by truncation is estimated. The presented numerical examples illustrate the use of the model for the elimination of the negative effects of emergency information service overload based on the filtering of the input flow of calls.Sergey StepanovMikhail StepanovMDPI AGarticleemergency servicesperformance evaluationrepeated callsMarkov processsystem of state equationsrecursive algorithmsMathematicsQA1-939ENMathematics, Vol 9, Iss 2811, p 2811 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	emergency services performance evaluation repeated calls Markov process system of state equations recursive algorithms Mathematics QA1-939
spellingShingle	emergency services performance evaluation repeated calls Markov process system of state equations recursive algorithms Mathematics QA1-939 Sergey Stepanov Mikhail Stepanov Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation
description	The model of a fully available group of servers with a Poisson flow of primary calls and the possibility of losses before and after occupying a free server is considered. Additionally, a call can leave the system because of the aging of transmitted information. After each loss, there is some probability that a customer repeats the call. Such models are seen in the modeling of various telecommunication systems such as emergency information services, call and contact centers, access nodes, etc., functioning in overloading situations. The stationary behavior of the system is described by the infinite-state Markov process. It is shown that stationary characteristics of the model can be calculated with the help of an auxiliary model of the same class but without call repetitions due to losses occurring before and after the occupation of a free server and the aging of transmitted information. The performance measurements of the auxiliary model are calculated by solving a system of state equations using a recursive algorithm based on the concept of the truncation of the used state space. This approach allows significant savings of computer resources to be made by ignoring highly unlikely states in the process of calculation. The error caused by truncation is estimated. The presented numerical examples illustrate the use of the model for the elimination of the negative effects of emergency information service overload based on the filtering of the input flow of calls.
format	article
author	Sergey Stepanov Mikhail Stepanov
author_facet	Sergey Stepanov Mikhail Stepanov
author_sort	Sergey Stepanov
title	Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation
title_short	Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation
title_full	Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation
title_fullStr	Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation
title_full_unstemmed	Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation
title_sort	estimation of the performance measures of a group of servers taking into account blocking and call repetition before and after server occupation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/4da7ad8108274e19969bcf2435a4a4b2
work_keys_str_mv	AT sergeystepanov estimationoftheperformancemeasuresofagroupofserverstakingintoaccountblockingandcallrepetitionbeforeandafterserveroccupation AT mikhailstepanov estimationoftheperformancemeasuresofagroupofserverstakingintoaccountblockingandcallrepetitionbeforeandafterserveroccupation
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Estimation of the Performance Measures of a Group of Servers Taking into Account Blocking and Call Repetition before and after Server Occupation

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