MRSPN analysis of Semi-Markovian finite source retrial queues

Ikhlef, Lyes; Lekadir, Ouiza; Aı̈ssani, Djamil

doi:10.1007/s10479-015-1883-8

Cited by 10 publications

(4 citation statements)

References 35 publications

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“…Pour simplifier cette procédure, plusieurs progiciels ont été développés et utilisés efficacement pour l'évaluation de la performance de systèmes complexes (voir par exemple, (Gharbi et Dutheillet 2011 ;Gharbi et Ioualalen 2006 ;Gharbi et al 2015 ;Gharbi et al 2014 ;Ikhlef et al 2016)). Dans le cadre de nos recherches, un outil logiciel similaire appelé MOSEL (Modeling, Specification and Evaluation Language) a été utilisé pour formuler le modèle et obtenir les mesures de performance.…”

Section: Système M/m/1unclassified

Résultats récents en files d’attente avec rappels à sources finies avec collisions

Nazarov¹,

Sztrik²,

Kvach³

2021

Théorie Des Files D’attente 1

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L’objectif de ce chapitre est de donner un aperçu des résultats récents sur les systèmes de files d’attente avec rappel à source finie à serveur unique avec collision de clients. Il s’agit notamment de déterminer lorsque le serveur est fiable et de modéliser les pannes et les réparations aléatoires du serveur selon qu’il est inactif ou occupé. Les méthodes numériques, de simulation et asymptotiques, assistées par des outils, sont considérées sous la condition d’un nombre croissant et illimité de sources.

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Section: Système M/m/1unclassified

Résultats récents en files d’attente avec rappels à sources finies avec collisions

Nazarov¹,

Sztrik²,

Kvach³

2021

Théorie Des Files D’attente 1

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“…Since in practice some components of the systems are subject to random breakdowns it is of basic importance to study reliability of retrial queues with server's breakdowns and repairs. Finite-source retrial queues with an unreliable server have been investigated in several recent papers, see for example Almási et al (2005); Dragieva (2014); Gharbi and Dutheillet (2011); Ikhlef et al (2016); Roszik (2004); Wang et al (2010Wang et al ( , 2011 and Zhang and Wang (2013).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Nazarov

Sztrik

Kvach

et al. 2021

Methodol Comput Appl Probab

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This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. A significant difference of this system from the previous ones is that the service time is assumed to follow a general distribution while the server’s lifetime and repair time is supposed to be exponentially distributed. The considered system is investigated by the method of asymptotic analysis under the condition of an unlimited growing number of sources. As a result, it is proved that the limiting probability distribution of the number of customers in the system follows a Gaussian distribution with given parameters. The Gaussian approximation and the estimations obtained by stochastic simulations of the prelimit probability distribution are compared to each other and measured by the Kolmogorov distance. Several examples are treated and figures show the accuracy and area of applicability of the proposed asymptotic method.

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“…This can be done by means of finite-source, or quasi-random input models. Retrial queues with quasirandom input are recent interest in modeling magnetic disk memory systems, cellular mobile networks, computer networks, and local-area networks with non-persistent CSMA/CD protocols, with star topology, with random access protocols, and with multiple-access protocols, see, for example Alfa and Isotupa (2004), Ali and Wei (2015), Almási et al (2016), Do et al (2014), Dragieva (2016), Ikhlef et al (2016) and Wüchner et al (2010).…”

Section: Introductionmentioning

confidence: 99%

Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs

et al. 2019

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The aim of the present paper is to investigate the steady-state distribution of response and waiting time in a finite-source M / M / 1 retrial queuing system with collision of customers where the server is subjects to random breakdowns and repairs depending on whether it is idle or busy. An asymptotic method is applied under the condition that the number of sources tends to infinity, the primary request generation rate, retrial rate tend to zero while service rate, failure rates, repair rate are fixed. As the result of the analysis it is shown that the steady-state probability distribution of the number of transitions/retrials of the customer into the orbit is geometric with a given parameter, and the normalized sojourn time of the customer in the system follows a generalized exponential distribution. It is also proved that the limiting distributions of the normalized sojourn time of the customer in the system and the normalized sojourn/waiting time of the customer in the orbit coincide. The novelty of this investigation is the introduction of failure and repair of the server. Approximations of prelimit distributions obtained with the help of stochastic simulation by asymptotic one are considered and several illustrative examples show the accuracy and range of applicability of the proposed asymptotic method.

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MRSPN analysis of Semi-Markovian finite source retrial queues

Cited by 10 publications

References 35 publications

Résultats récents en files d’attente avec rappels à sources finies avec collisions

Résultats récents en files d’attente avec rappels à sources finies avec collisions

Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs

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