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Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process


  • Ward Whitt

    (Bell Laboratories, Holmdel, New Jersey 07733)


This paper cautions against using only the equilibrium distribution to describe the behavior of a queue. It is suggested that fluctuations in the queue-length process should also be described, for example, by various first-passage-time distributions. The range of possible fluctuations associated with a given equilibrium queue-length distribution is described for the GI/M/1 queue. The theory of complete Tchebycheff systems in Karlin and Studden [Karlin, S., W. J. Studden. 1966. Tchebycheff systems: with applications in analysis and statistics. John Wiley and Sons, New York.] is applied to construct appropriate extremal distributions, i.e., interarrival-time distributions having the given equilibrium queue-length distribution and maximum or minimum values of fluctuation measures such as the relaxation time.

Suggested Citation

  • Ward Whitt, 1983. "Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process," Management Science, INFORMS, vol. 29(4), pages 395-408, April.
  • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:4:p:395-408

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    Cited by:

    1. Iosif Pinelis, 2016. "On the extreme points of moments sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 325-349, June.

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    queues; stochastic models; applied probability;


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