Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

Bouchentouf, Amina Angelika; Guendouzi, Abdelhak; Houalef, Meriem; Majid, Shakir

doi:10.37190/ord220202

Cited by 3 publications

(2 citation statements)

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“…Tian et al [4] reviewed the research on working vacation queueing systems. Recently, the survey on the works of queues with working vacation has been reported by [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Liu

Hsu

et al. 2023

Computation

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This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.

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Section: Introductionmentioning

confidence: 99%

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Liu

Hsu

et al. 2023

Computation

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“…Further, an optimal value of slow service rate is estimated using a quadratic fit search approach. Bouchentouf et al [10] analyzed an M/M/1 queueing model under single and multiple vacation policies with balking, reneging, and multi-phase random environment and obtained steady-state probabilities using the probability generating function method.…”

Section: Introductionmentioning

confidence: 99%

Optimization of M/M/2 Queueing Model with Working Vacations

2023

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The paper deals with an M/M/2 Queueing Model with working vacations and reneging of customers due to impatience. The matrix geometric method is used to find the distribution of the number of customers in the system. A cost function is constructed to obtain the optimal value of the service rate to optimize (minimize) the cost function using the Quadratic Fit Search Method (QFSM). Further, the effects on the system's performance measures using numerical analysis and graphical representation are studied.

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A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption

et al. 2023

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This paper deals with a M/M/c queueing system with waiting servers, balking, reneging, and K-variant working vacations subjected to Bernoulli schedule vacation interruption. Whenever the system is emptied, the servers wait for a while before synchronously going on vacation during which services are offered with a lower rate. We obtain the steady-state probabilities of the system using the matrix-geometric method. In addition, we derive important performance measures of the queueing model. Moreover, we construct a cost model and apply a direct search method to get the optimum service rates during both working vacation and regular working periods at lowest cost. Finally, numerical results are provided.

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Analysis of a single server queue in a multi-phase random environment with working vacations and customers’ impatience

Cited by 3 publications

References 0 publications

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Preemptive Priority Markovian Queue Subject to Server Breakdown with Imperfect Coverage and Working Vacation Interruption

Optimization of M/M/2 Queueing Model with Working Vacations

A matrix geometric solution of a multi-server queue with waiting servers and customers’ impatience under variant working vacation and vacation interruption

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