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Queuing with Multiple Poisson Inputs and Exponential Service Times

Author

Listed:
  • C. J. Ancker

    (System Development Corporation, Santa Monica, California)

  • A. V. Gafarian

    (System Development Corporation, Santa Monica, California)

Abstract

This paper contains an analysis of a single-server queuing system for m different types of customers having independent Poisson arrivals with rates (lambda) ı , ı = 1, ..., m and exponential service times with rates (mu) ı , ı = 1, ..., m . The discipline is first-come, first-served. Some derived results are (a) a recursion relation for the steady-state probability of n in queue, (b) a recursion relation for the steady-state probability that some member of a particular class is in service and that n of any class are in queue, and (c) the characteristic equation for the waiting-time distribution and its general inversion for the two-population case. The recursion relations are simple for computational purposes.

Suggested Citation

  • C. J. Ancker & A. V. Gafarian, 1961. "Queuing with Multiple Poisson Inputs and Exponential Service Times," Operations Research, INFORMS, vol. 9(3), pages 321-327, June.
    • Handle: RePEc:inm:oropre:v:9:y:1961:i:3:p:321-327
    DOI: 10.1287/opre.9.3.321
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    Cited by:

    1. Chydzinski, Andrzej, 2022. "Per-flow structure of losses in a finite-buffer queue," Applied Mathematics and Computation, Elsevier, vol. 428(C).

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