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The analysis of MX/M/1 queue with two-stage vacations policy

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  • Qingqing Ye

Abstract

In this article, we consider a batch arrival MX/M/1 queue with two-stage vacations policy that comprises of single working vacation and multiple vacations, denoted by MX/M/1/SWV + MV. Using the matrix analytic method, we derive the probability generating function (PGF) of the stationary system size and investigate the stochastic decomposition structure of stationary system size. Further, we obtain the Laplace–Stieltjes transform (LST) of stationary sojourn time of a customer by the first passage time analysis. At last, we illustrate the effects of various parameters on the performance measures numerically and graphically by some numerical examples.

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  • Qingqing Ye, 2019. "The analysis of MX/M/1 queue with two-stage vacations policy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(18), pages 4492-4510, September.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:18:p:4492-4510
    DOI: 10.1080/03610926.2018.1483514
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    Cited by:

    1. Kumar, Anshul & Jain, Madhu, 2023. "Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 259-281.

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