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Analytical Distribution of Waiting Time in the M/{iD}/1 Queue

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Abstract

We give an analytical formula for the steady-state distribution of queue-wait in the M/G/1 queue, where the service time for each customer is a positive integer multiple of a constant D > 0. We call this an M/{iD}/1 queue. We give numerical algorithms to calculate the distribution. In addition, in the case that the service distribution is sparse, we give revised algorithms that can compute the distribution more quickly.

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Authors and Affiliations

  1. Systems Engineering and Operations Research, George Mason University, 4400 University Dr. MS 4A6, Fairfax, VA, 22030

    John F. Shortle

  2. Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada, N9B 3P4

    Percy H. Brill

Authors
  1. John F. Shortle
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  2. Percy H. Brill
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Correspondence to John F. Shortle.

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AMS subject classification: 60K25, 90B22

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Shortle, J.F., Brill, P.H. Analytical Distribution of Waiting Time in the M/{iD}/1 Queue. Queueing Syst 50, 185–197 (2005). https://doi.org/10.1007/s11134-005-0615-1

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  • DOI: https://doi.org/10.1007/s11134-005-0615-1

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