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A Queueing Problem in Which Customers Have Different Service Distributions

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  • T. W. R. Collings

Abstract

A single‐server queue is examined whose customers can be categorized into k groups. For the ith group : (1) Arrivals follow a Poisson distribution, the average arrival rate per unit time being λi. (2) The service time follows the exponential distribution with average service time equal to 1/μi. Using a method of “cuts”, the recurrence relations between states of the queueing system are examined. The equilibrium probabilities of queue size are found and it is shown that the approximation of a group of exponential service distributions by a single exponential distribution, having a mean equal to that of the group, always underestimates the mean queue size.

Suggested Citation

  • T. W. R. Collings, 1974. "A Queueing Problem in Which Customers Have Different Service Distributions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(1), pages 75-82, March.
    • Handle: RePEc:bla:jorssc:v:23:y:1974:i:1:p:75-82
    DOI: 10.2307/2347057
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