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The M -Server Queue with Poisson Input and Gamma-Distributed Service of Order Two

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  • Saul Shapiro

    (International Business Machines, Inc., Yorktown Heights, New York)

Abstract

Analysis is made of the multiserver-queuing systems with Poisson input and service times distributed according to a second order gamma distribution. A set of difference equations involving the time-invariant state-probabilities is derived and a unique solution of these equations is found. The method used is that of treating the gamma-distributed service times or order two as the sum of two independent and identically distributed service times, which are exponentially distributed. It is shown that the time invariant probability of n customers being in the system is of the form, P n = ∑ i =0 i = m C i β i n , where m is the number of servers, and a method for finding the C i 's and β i 's is given.

Suggested Citation

  • Saul Shapiro, 1966. "The M -Server Queue with Poisson Input and Gamma-Distributed Service of Order Two," Operations Research, INFORMS, vol. 14(4), pages 685-694, August.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:4:p:685-694
    DOI: 10.1287/opre.14.4.685
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    Cited by:

    1. V Marianov & T B Boffey & R D Galvão, 2009. "Optimal location of multi-server congestible facilities operating as M/E r /m/N queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 674-684, May.
    2. Adan, Ivo & de Kok, Ton & Resing, Jacques, 1999. "A multi-server queueing model with locking," European Journal of Operational Research, Elsevier, vol. 116(2), pages 249-258, July.

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