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

doi:10.1007/s40305-021-00384-3

Abstract

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.

Key words: Queueing models, Random environment, Working vacation policy, Impatient customers, Probability generating function, Optimization

CLC Number:

Meriem Houalef, Amina Angelika Bouchentouf, Lahcene Yahiaoui. A Multi-server Queue in a Multi-phase Random Environment with Waiting Servers and Customers' Impatience Under Synchronous Working Vacation Policy[J]. Journal of the Operations Research Society of China, 2023, 11(3): 459-487.

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