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MAP/M/c and M/PH/c queues with constant impatience times

Author

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  • Ken’ichi Kawanishi

    (Gunma University)

  • Tetsuya Takine

    (Osaka University)

Abstract

This paper considers stationary MAP/M/c and M/PH/c queues with constant impatience times. In those queues, waiting customers leave the system without receiving their services if their elapsed waiting times exceed a predefined deterministic threshold. For the MAP/M/c queue with constant impatience times, Choi et al. (Math Oper Res 29:309–325, 2004) derive the virtual waiting time distribution, from which the loss probability and the actual waiting time distribution are obtained. We first refine their result for the virtual waiting time and then derive the stationary queue length distribution. We also discuss the computational procedure for performance measures of interest. Next we consider the stationary M/PH/c queue with constant impatience times and derive the loss probability, the waiting time distribution, and the queue length distribution. Some numerical results are also provided.

Suggested Citation

  • Ken’ichi Kawanishi & Tetsuya Takine, 2016. "MAP/M/c and M/PH/c queues with constant impatience times," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 381-420, April.
    • Handle: RePEc:spr:queues:v:82:y:2016:i:3:d:10.1007_s11134-015-9455-9
    DOI: 10.1007/s11134-015-9455-9
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    References listed on IDEAS

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    1. Daniel P. Heyman & Shaler Stidham, 1980. "The Relation between Customer and Time Averages in Queues," Operations Research, INFORMS, vol. 28(4), pages 983-994, August.
    2. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    3. P. H. Brill & M. J. M. Posner, 1977. "Level Crossings in Point Processes Applied to Queues: Single-Server Case," Operations Research, INFORMS, vol. 25(4), pages 662-674, August.
    4. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Ordered Service," Operations Research, INFORMS, vol. 5(5), pages 650-656, October.
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    Cited by:

    1. Anders Rygh Swensen, 2023. "Remaining Loads in a PH/M/c Queue with Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-15, March.

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