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A Discrete-Time Queue with Balking, Reneging, and Working Vacations

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  • Veena Goswami

Abstract

This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.

Suggested Citation

  • Veena Goswami, 2014. "A Discrete-Time Queue with Balking, Reneging, and Working Vacations," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-8, October.
    • Handle: RePEc:hin:jnijsa:358529
    DOI: 10.1155/2014/358529
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    Cited by:

    1. Amina Angelika Bouchentouf & Mouloud Cherfaoui & Mohamed Boualem, 2019. "Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 300-323, March.

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