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A Multi-server Queue in a Multi-phase Random Environment with Waiting Servers and Customers’ Impatience Under Synchronous Working Vacation Policy

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Abstract

In this paper, we develop an M/M/c queueing system in a Markovian environment with waiting servers, balking and reneging, under both synchronous single and multiple working vacation policies. When the system is in operative phase j,  \(j=\overline{1,K},\) customers are served one by one. Once the system is empty, the servers have to wait a random period of time before leaving, causing the system to move to vacation phase 0 at which new arrivals can be served at lower rate. Using the method of the probability generating functions, we establish the steady-state analysis of the system. Special cases of the queueing model are presented. Then, explicit expressions of the useful system characteristics are derived. In addition, a cost model is constructed to define the optimal values of service rates, simultaneously, to minimize the total expected cost per unit time via a quadratic fit search method. Numerical examples are provided to display the impact of different system characteristics.

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Authors and Affiliations

  1. Mathematics Laboratory, University of Sidi Bel Abbes, Ecole Supérieure En Sciences Appliquées, Tlemcen, 13000, Algeria

    Meriem Houalef

  2. Mathematics Laboratory, Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, 22000, Algeria

    Amina Angelika Bouchentouf

  3. Laboratory of Stochastic Models, Statistic and Applications, University of Saida-Dr. Moulay Tahar, B. P. 138, En-Nasr, Saida, Algeria

    Lahcene Yahiaoui

Authors
  1. Meriem Houalef
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  2. Amina Angelika Bouchentouf
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  3. Lahcene Yahiaoui
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Houalef, M., Bouchentouf, A.A. & Yahiaoui, L. A Multi-server Queue in a Multi-phase Random Environment with Waiting Servers and Customers’ Impatience Under Synchronous Working Vacation Policy. J. Oper. Res. Soc. China 11, 459–487 (2023). https://doi.org/10.1007/s40305-021-00384-3

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  • DOI: https://doi.org/10.1007/s40305-021-00384-3

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