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The Markovian Queue with Bounded Waiting time

Author

Listed:
  • Bezalel Gavish

    (University of Rochester)

  • Paul J. Schweitzer

    (IBM Thomas J. Watson Research Center, Yorktown Heights)

Abstract

The single-server queueing system is studied where arrivals are rejected if their waiting plus service times would exceed a fixed amount K. Applications of this model include equipment repair facilities and buffered communication devices with constant discharge rate receiving messages from a high-speed data channel. A procedure for computing the equilibrium behavior is described for the case of random arrivals and arbitrary service time requirements. Detailed analytic results and graphs are given for the case of exponentially distributed service time requirements, including the server utilization, rejection probability, mean time in system, mean server busy period, and the mean and probability density function of the virtual waiting time.

Suggested Citation

  • Bezalel Gavish & Paul J. Schweitzer, 1977. "The Markovian Queue with Bounded Waiting time," Management Science, INFORMS, vol. 23(12), pages 1349-1357, August.
    • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:12:p:1349-1357
    DOI: 10.1287/mnsc.23.12.1349
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    Cited by:

    1. Brill, P.H. & Huang, M.L. & Hlynka, M., 2020. "On the service time in a workload-barrier M/G/1 queue with accepted and blocked customers," European Journal of Operational Research, Elsevier, vol. 283(1), pages 235-243.
    2. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    3. Susan H. Xu & Long Gao & Jihong Ou, 2007. "Service Performance Analysis and Improvement for a Ticket Queue with Balking Customers," Management Science, INFORMS, vol. 53(6), pages 971-990, June.
    4. Dijk, N.M. van, 1989. "A note on extended uniformization for non-exponential stochastic networks," Serie Research Memoranda 0026, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    5. Baris Ata & Peter W. Glynn & Xiaoshan Peng, 2017. "An equilibrium analysis of a discrete-time Markovian queue with endogenous abandonments," Queueing Systems: Theory and Applications, Springer, vol. 86(1), pages 141-212, June.
    6. Bert Zwart, 2015. "Loss rates in the single-server queue with complete rejection," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 299-315, June.

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