Method of asymptotic semiinvariants for studying a mathematical model of a random access network

Nazarov, Anatoly; Sudyko, E. A.

doi:10.1134/s0032946010010072

Cited by 10 publications

(3 citation statements)

References 3 publications

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“…Dans ce qui suit, nous montrons comment nous pouvons obtenir la distribution à l'aide de la fonction caractéristique inverse (voir (Nazarov et Sudyko 2010)).…”

Section: Exemplaire Réservé à Janos Sztrikunclassified

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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“…Dans ce qui suit, nous montrons comment nous pouvons obtenir la distribution à l'aide de la fonction caractéristique inverse (voir (Nazarov et Sudyko 2010)).…”

Section: Exemplaire Réservé à Janos Sztrikunclassified

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 it is very complicated to get the exact solution of this system, we will use asymptotics methods. Let us investigate this system in two stages as the authors carried in Kvach and Nazarov [20], Nazarov and Sudyko [23], Nazarov and Sudyko [24], Nazarov and Moiseeva [22].…”

Section: Asymptotic Analysis Of the Distribution Of The Server's Statmentioning

confidence: 99%

Asymptotic Waiting Time Analysis of a Finite-Source M/M/1 Retrial Queueing System

Sudyko¹,

Nazarov²,

Sztrik³

2018

Prob. Eng. Inf. Sci.

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The aim of the paper is to derive the distribution of the number of retrial of the tagged request and as a consequence to present the waiting time analysis of a finite-source M/M/1 retrial queueing system by using the method of asymptotic analysis under the condition of the unlimited growing number of sources. As a result of the investigation, it is shown that the asymptotic distribution of the number of retrials of the tagged customer in the orbit is geometric with given parameter, and the waiting time of the tagged customer has a generalized exponential distribution. For the considered retrial queuing system numerical and simulation software packages are also developed. With the help of several sample examples the accuracy and range of applicability of the asymptotic results in prelimit situation are illustrated showing the effectiveness of the proposed approximation.

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“…The aim of the present paper is to investigate such systems which has the above mention properties, that is finite-source, retrial, collisions, and non-reliability of the server. The present model is a generalization of the systems treated in Kvach and Nazarov (2015), Nazarov et al (2014), Nazarov and Sudyko (2010), Nazarov and Moiseeva (2006) and Sudyko et al (2018) and it is the natural continuation of the paper in which the asymptotic distribution of the number of customers in the system has been investigated.…”

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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Method of asymptotic semiinvariants for studying a mathematical model of a random access network

Cited by 10 publications

References 3 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 Waiting Time Analysis of a Finite-Source M/M/1 Retrial Queueing System

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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