Untold Horrors of the Waiting Room: What the Equilibrium Distribution Will Never Tell About the Queue-Length Process
警告不要仅用均衡分布描述排队行为，建议同时描述排队长度过程的波动，例如通过首次通过时间分布，并针对GI/M/1队列描述了与给定均衡排队长度分布相关的可能波动范围。
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.