Untold Horrors of the Waiting Room: What The Equilibrium Distribution Will Never Tell About the Queue-Length Process
Article Abstract:
It is common to describe a queue by giving the mean equilibrium distribution. The variance and-or tail probabilities are also given sometimes. However, in addition to the equilibrium distibution, it is useful to describe the fluctuations or transient behavior of the stochastic process. The transient behavior is important because it can contribute to the cost-benefits of operating a system. The limitations of the equilibrium distribution is illustrated with the GI-M-1 queue. The queue-length equilibrium is assumed known so that one can determine traffic intensity, arrival rate, and service rate. All renewal arrival processes can be characterized. Two external distributions are identified. One maximizes long-run fluctuations and the other short-run fluctuations. Those interarrival-time distributions describe the range of possible values for several different fluctuation measures. A graph shows Relaxation-Time equations.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1983
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The Best Order For Queues in Series
Article Abstract:
An important design problem for queueing systems is to determine the best order for two or more service stations in series. For given external arrival process and given service-time distributions, the object is to determine the order of the stations (to be used by all customers) that minimizes the expected equilibrium sojourn time per customer. Unfortunately, very little is known about this problem because exact analysis is extremely difficult. This paper applies approximation methods recently developed for networks of queues to obtain approximation formulas and useful heuristic design principles. (Reprinted by Permission of Publisher.)
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1985
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Arranging queues in series: a simulation experiment
Article Abstract:
Simulations of two queues were used to investigate the design of infinite-capacity single-server queues, as well as congestion in non-Markov open queueing networks. The results indicated that the order of queues was more important when the variability of service-time distributions was considerable. Parametric-decomposition approximations of steady-state performance measures of non-Markov open queuing networks appeared to provide relatively accurate estimates of the importance of order.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1990
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