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An Approximation for the Moments of Waiting Times

Author

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  • C. R. Heathcote

    (Australian National University, Canberra, Australia)

  • P. Winer

    (Australian National University, Canberra, Australia)

Abstract

Methods are available for computing properties of the waiting time associated with a variety of single-server queuing models in the equilibrium state. Since these calculations are more difficult in the time-dependent case, this paper develops an approximation procedure applicable to a wide class of single-server queues. Specifically, it considers the moments of the waiting time W n of the n th arriving customer of the system GI / G /1 and (given certain conditions) uses an expansion related to the central limit theorem to derive approximations to these moments. The expectation EW n is treated in some detail, particularly for the Erlang system E k / E m /1, and numerical illustrations are given. The same arguments apply to higher moments, but the calculations become tedious and details are not given.

Suggested Citation

  • C. R. Heathcote & P. Winer, 1969. "An Approximation for the Moments of Waiting Times," Operations Research, INFORMS, vol. 17(1), pages 175-186, February.
    • Handle: RePEc:inm:oropre:v:17:y:1969:i:1:p:175-186
    DOI: 10.1287/opre.17.1.175
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