Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process
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.
Volume (Year): 29 (1983)
Issue (Month): 4 (April)
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