Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers

Bouchentouf, Amina Angelika; Cherfaoui, Mouloud; Boualem, Mohamed

doi:10.1007/s12597-019-00357-4

Cited by 30 publications

(11 citation statements)

References 23 publications

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“…Over the past few years, queueing models with Bernoulli feedback have increasingly attracted the attention of many researchers [9]- [14]. Taking into account the feedback effect makes it possible to bring the considered models closer to a real situation, where the claims once serviced may require repeat service for different reasons.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Bouchentouf

Medjahri

Boualem

et al. 2022

Discrete and Continuous Models

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In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.

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Section: Introductionmentioning

confidence: 99%

“…This paper contributes in this sense. In fact, only a few research papers have been done treating this case [9]- [12], [30].…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Bouchentouf

Medjahri

Boualem

et al. 2022

Discrete and Continuous Models

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“…Therefore, it has generated a fundamental results with extensive bibliographical references on this area (cf. Zhang et al [41], Altman and Yechaili [2,3], Ke [16], Ke et al [17], Adan et al [1], Yue et al [37], Ammar [4], Laxmi and Rajesh [33], Bouchentouf et al [9,10], and Kumar [20]).…”

Section: Introductionmentioning

confidence: 99%

Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

Bouchentouf

Boualem

Cherfaoui

et al. 2021

YUGOSLAV J OPERATION

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We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server's states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system.

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“…Wang et al [32] surveyed the queueing systems with impatient customers in accordance with various dimensions. Bouchentouf et al [33] analyzed a finite capacity single server M/M/1/N feedback queueing system with vacation, balking, reneging and retention of reneged customers and they obtained important measures of effectiveness of the model by using the stationary distribution. Bhardwaj et al [34] considered a queueing system with impatient customers under fuzzy environment.…”

Section: Introductionmentioning

confidence: 99%

Optimization of M/M/s/N Queueing Model with Reneging in a Fuzzy Environment

Panta¹,

Ghimire²,

Panthi³

et al. 2021

AJOR

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This paper deals with the study of multi-server queueing model in a fuzzy environment with imposition of reneging of customers. Entry of the customers in the system is assumed to be Poisson process and exponential service time distribution under first-come-first-served basis. Specific of this investigation is to derive the various fuzzy performance measures such as fuzzy queue length, fuzzy waiting time in queue, fuzzy response time and fuzzy optimal number of servers in explicit form for the finite capacity multi-server queueing system by using recursive method. For the validity of the model we have obtained the numerical illustrations in tabular form which shows that fuzzy-queue can be more realistic than crisp queue.

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Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers

Cited by 30 publications

References 23 publications

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

Optimization of M/M/s/N Queueing Model with Reneging in a Fuzzy Environment

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