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1 results

  • Waiting time and workload in queues with periodic Poisson input

  • Austin J. Lemoine
  • Journal:
    Journal of Applied Probability / Volume 26 / Issue 2 / June 1989
    Published online by Cambridge University Press:
    14 July 2016, pp. 390-397
    Print publication:
    June 1989

  • This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].