Asymptotic Analysis of Closed Markov Retrial Queuing System with Collision

Nazarov, Anatoly; Kvach, Anna; Yampolsky, Vladimir

doi:10.1007/978-3-319-13671-4_38

Cited by 20 publications

(13 citation statements)

References 3 publications

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“…In this paper, we will investigate the distribution of the number of retrials of a customer together with the distribution of the waiting time of a request in a RQ-system since they are connected to each other. Related results can be found, for example in Alfa and Isotupa [1], Dragieva [10], Dragieva [11], Falin and Artalejo [13], Gharbi and Dutheillet [14], Kvach and Nazarov [20], Nazarov, Kvach and Yampolsky [25], Nazarov and Sudyko [22], Wang, Zhao and Zhang [29], Wang, Zhao and Zhang [30], Zhang and Wang [32]. We will use the method of asymptotic analysis under limiting condition of a growing number of sources as it has been applied, for example in Kvach and Nazarov [20], Nazarov, Kvach and Yampolsky [25], Nazarov and Moiseeva [22].…”

Section: Introductionmentioning

confidence: 56%

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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Section: Introductionmentioning

confidence: 56%

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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“…Investigating and building up efficient procedures for preventing conflicts and corresponding message delays are needed. Of course, there are papers that have studied retrial queues with collisions see for example [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

Sztrik

Tóth

Danilyuk

et al. 2021

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

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In this paper, we consider a retrial queueing system of M/G/1 type with an unreliable server, collisions, and impatient customers. The novelty of our work is to carry out a sensitivity analysis applying different distributions of service time of customers on significant performance measures for example on the probability of abandonment, the mean waiting time of an arbitrary, successfully served, impatient customer, etc. A customer is able to depart from the system in the orbit if it does not get its appropriate service after a definite random waiting time so these will be the so-called impatient customers. In the case of server failure, requests are allowed to enter the system but these will be forwarded immediately towards the orbit. The service, retrial, impatience, operation, and repair times are supposed to be independent of each other. Several graphical illustrations demonstrate the comparisons of the investigated distributions and the interesting phenomena which are obtained by our self-developed simulation program. The achieved results are compared to the results of the [2] to check how the system characteristics changes if we use other distributions of service time and to present the advantages of performing simulations in certain scenarios.

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“…An essential matter is to develop workable procedures for allaying the conflict and corresponding message delay. There have been recent results on retrial queues with collision in [1,4,[9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Simulation of Finite-Source Retrial Queueing Systems with Collisions and Non-reliable Server

Tóth

Bérczes

Sztrik

et al. 2017

Communications in Computer and Information Science

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Abstract. The aim of the present paper is to build a simulation program to investigate finite-source retrial queuing system with collision of the customers where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. All the random variables involved in the model construction are assumed to be independent and generally distributed. The novelty of the investigation is to carry sensitivity analysis of the performance measures using various distributions. Several figures show the effect of different distributions on the performance measures such as mean and variance of number of customers in the system, mean and variance of response time, mean and variance of time a customer spent in service, mean and variance of sojourn time in the orbit.

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Asymptotic Analysis of Closed Markov Retrial Queuing System with Collision

Cited by 20 publications

References 3 publications

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

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

Analysis of Retrial Queueing System M/G/1 with Impatient Customers, Collisions and Unreliable Server Using Simulation

Simulation of Finite-Source Retrial Queueing Systems with Collisions and Non-reliable Server

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