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The Output of an M / D /1 Queue

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  • Charles D. Pack

    (Bell Laboratories, Holmdel, New Jersey)

Abstract

In this paper we investigate the output process of the M / D /1 queuing system. We derive expressions for the distributions and first two moments, in both steady-state and transient conditions, of the following random variables: (1) the time until the n th departure measured from a departure epoch, T 0 , (2) the time between the n − 1st and n th departures after T 0 , and (3) the number of departures in ( T 0 , T 0 + t ]. Further we study the autocorrelation functions of random variables (1) and (2) in the steady state.

Suggested Citation

  • Charles D. Pack, 1975. "The Output of an M / D /1 Queue," Operations Research, INFORMS, vol. 23(4), pages 750-760, August.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:4:p:750-760
    DOI: 10.1287/opre.23.4.750
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    Cited by:

    1. J.P.C. Blanc, 2002. "Computation of Autocorrelations of Interdeparture Times by Numerical Transform Inversion," Annals of Operations Research, Springer, vol. 112(1), pages 83-100, April.
    2. Christos Zacharias & Mor Armony, 2017. "Joint Panel Sizing and Appointment Scheduling in Outpatient Care," Management Science, INFORMS, vol. 63(11), pages 3978-3997, November.

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