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Stationary Waiting Time Distribution of a Queue in Which Customers Require a Random Number of Servers

Author

Listed:
  • Prawit Ittimakin

    (AT&T Bell Laboratories, Holmdel, New Jersey)

  • Edward P. C. Kao

    (University of Houston, Houston, Texas)

Abstract

We consider the multiserver queueing system studied originally by L. Green (1980) in which customers request service from a random number of identical servers. We provide a matrix-geometric formulation of the problem, present a simple means for computing the stationary probability vector, and propose an algorithm based on randomization for computing the waiting time distribution. We also give a numerical example and discuss issues involved in extending the formulation to include customer priority classes.

Suggested Citation

  • Prawit Ittimakin & Edward P. C. Kao, 1991. "Stationary Waiting Time Distribution of a Queue in Which Customers Require a Random Number of Servers," Operations Research, INFORMS, vol. 39(4), pages 633-638, August.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:4:p:633-638
    DOI: 10.1287/opre.39.4.633
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    Citations

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    Cited by:

    1. Alexander Rumyantsev & Evsey Morozov, 2017. "Stability criterion of a multiserver model with simultaneous service," Annals of Operations Research, Springer, vol. 252(1), pages 29-39, May.
    2. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.
    3. Hall, Randolph, 2000. "Incident Dispatching, Clearance and Delay," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2pp689vn, Institute of Transportation Studies, UC Berkeley.
    4. Hall, Randolph W., 2002. "Incident dispatching, clearance and delay," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(1), pages 1-16, January.
    5. Hall, Randolph W., 2001. "Incident Management: Process Analysis and Improvement," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt1jf6j37t, Institute of Transportation Studies, UC Berkeley.

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