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Technical Note—On Waiting Times for a Queue in Which Customers Require Simultaneous Service from a Random Number of Servers

Author

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  • Andrew F. Seila

    (University of Georgia, Athens, Georgia)

Abstract

We consider a queueing system, first introduced by L. Green in 1980, in which customers from a Poisson arrival stream request simultaneous service from a random number of identical servers with exponential service times. Computational formulas for the second moment of time in queue are given, along with tables of these values for selected systems. Numerical results show that the coefficient of variation for time in queue is always greater than 1 and decreases with increasing congestion.

Suggested Citation

  • Andrew F. Seila, 1984. "Technical Note—On Waiting Times for a Queue in Which Customers Require Simultaneous Service from a Random Number of Servers," Operations Research, INFORMS, vol. 32(5), pages 1181-1184, October.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:5:p:1181-1184
    DOI: 10.1287/opre.32.5.1181
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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. Ansari, Sardar & Yoon, Soovin & Albert, Laura A., 2017. "An approximate hypercube model for public service systems with co-located servers and multiple response," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 143-157.
    4. Dijk, N.M. van & Smeitink, E., 1988. "A non-exponential queueing system with batch servicing," Serie Research Memoranda 0013, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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