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Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters

Author

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  • Jiang Tao

    (College of Economics and Management, Shandong University of Science and Technology, Qingdao, 266590, China)

Abstract

This paper considers a discrete-time Geo/G/1 queue in a multi-phase service environment, where the system is subject to disastrous breakdowns, causing all present customers to leave the system simultaneously. At a failure epoch, the server abandons the service and the system undergoes a repair period. After the system is repaired, it jumps to operative phase i with probability qi, i = 1, 2 ⋯, n. Using the supplementary variable technique, we obtain the distribution for the stationary queue length at the arbitrary epoch, which are then used for the computation of other performance measures. In addition, we derive the expected length of a cycle time, the generating function of the sojourn time of an arbitrary customer, and the generating function of the server’s working time in a cycle. We also give the relationship between the discrete-time queueing system to its continuous-time counterpart. Finally, some examples and numerical results are presented.

Suggested Citation

  • Jiang Tao, 2018. "Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters," Journal of Systems Science and Information, De Gruyter, vol. 6(4), pages 349-365, August.
    • Handle: RePEc:bpj:jossai:v:6:y:2018:i:4:p:349-365:n:5
    DOI: 10.21078/JSSI-2018-349-17
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    References listed on IDEAS

    as
    1. I. Atencia & P. Moreno, 2006. "A Discrete-Time Geo/ G/1 retrial queue with the server subject to starting failures," Annals of Operations Research, Springer, vol. 141(1), pages 85-107, January.
    2. R. Sudhesh & R. Sebasthi Priya & R. B. Lenin, 2016. "Analysis of N-policy queues with disastrous breakdown," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 612-634, October.
    3. George C. Mytalas & Michael A. Zazanis, 2015. "An MX/G/1 queueing system with disasters and repairs under a multiple adapted vacation policy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 171-189, April.
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