Analysis and Performance Evaluation of Markovian Feedback Multi-Server Queueing Model with Vacation and Impatience

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

doi:10.1080/01966324.2020.1842271

Cited by 15 publications

(6 citation statements)

References 25 publications

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“…where Next, by multiplying (15) and 16 19, so z = 1 must be the root of the numerator of the right hand side of equation (19). Thus, we get where This implies…”

Section: The Equilibrium State Distributionmentioning

confidence: 96%

“…Using repeatedly equation 23, we obtain Substituting equations (22) and (24) into (19) and 20, respectively, we get and From equations (25)-(26), we find the expression of the probability generating function G j (z), for j = 0, K − 1 in terms of P 0,0 , and from equation 22, we have P 0,K in terms of P 0,0 . While P 0,j in terms of P 0,0 is given in equation (24).…”

Section: The Equilibrium State Distributionmentioning

confidence: 99%

“…These queues have extensively examined (cf. Zhang et al [12], Altman and Yechiali [13], Yue et al [14], Altman and Yechiali [15], Adan et al [16], Ammar [17], and Bouchentouf et al [18,19]).…”

Section: Introductionmentioning

confidence: 99%

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Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers

Bouchentouf

Guendouzi

2021

SN Oper. Res. Forum

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We consider an infinite capacity batch arrival single server Markovian Bernoulli feedback queueing system with waiting server, K-variant vacations, impatient customers and retention of reneged customers. The model is analyzed using probability generating function (PGF) technique. Various queueing system characteristics are derived. Then, by setting the appropriate parameters, some special cases are discussed. Moreover, a cost model for the queueing system is developed. The parameter optimization is numerically illustrated using particle swarm optimization (PSO). Finally, numerical results are provided to explore the impact of system parameters on performance measures and costs of the queueing system.

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“…where Next, by multiplying (15) and 16 19, so z = 1 must be the root of the numerator of the right hand side of equation (19). Thus, we get where This implies…”

Section: The Equilibrium State Distributionmentioning

confidence: 96%

Section: The Equilibrium State Distributionmentioning

confidence: 99%

See 1 more Smart Citation

Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers

Bouchentouf

Guendouzi

2021

SN Oper. Res. Forum

Self Cite

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“…Multi-server ensures that maximum entity disposed of with service (Bedewy et al, 2016). An empty system indicates that the idle time of the servers is high (Bouchentouf et al, 2021) and a short queue length is the result of large inter-arrival times (Kempa and Kurzyk, 2022).…”

Section: Introductionmentioning

confidence: 99%

Formulation and Performance Assessment for Multiple Server Queueing Models

Alam¹,

Azrin²,

U³

et al. 2023

Preprint

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Queueing theory has grown in prominence as it provides the numerical foundation for decision-making assessment. Queueing models with multiple servers provide extensive decision-making data, which is critical for evaluating a server's performance. The purpose of this study is to formulate multiple server queueing models and provides a performance assessment to evaluate the appropriate models. A three-phased structured approach has been used to model and analyze performance for multiple server queueing models. The "Multiple Server Finite Queue Length Infinite Queue Population Model" is most desirable for a customer who has to wait for less time (approximately 43.14%) in the system as well as in the queue (approximately 62.16%) and reduces the system length by approximately 47.02% and the queue length by approximately 64.76%. However, the "Multiple Server Infinite Queue Length Infinite Queue Population Model" is preferable from a managerial perspective, as the "Multiple Server Finite Queue Length Infinite Queue Population Model" has fewer customers in the system, indicating a loss from a managerial standpoint. When the arrival rate of customers, service rate, and the number of servers are increased, length of the system and queue remain nearly constant, whereas the waiting time in the system nearly doubles for both queueing models. The paper develops a performance evaluation of the “Multiple Server Infinite Queue Length Infinite Queue Population Model” and “Multiple Server Finite Queue Length Infinite Queue Population Model”, which are capable of adapting to an unpredictable decision in any service system. Furthermore, this study provides decision-makers with a perspective-based evaluation of the mentioned servers, with a focus on a manager and a customer.

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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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Analysis and Performance Evaluation of Markovian Feedback Multi-Server Queueing Model with Vacation and Impatience

Cited by 15 publications

References 25 publications

Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers

Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers

Formulation and Performance Assessment for Multiple Server Queueing Models

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

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