Queue Length Dependent Priority Queues

K. R. Balachandran
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K. R. Balachandran: The University of Wisconsin-Milwaukee

Management Science, 1971, vol. 17, issue 7, 463-471

Abstract: Priority rules that are mixtures of pre-emption and postponable rules are analyzed. Whether a pre-emption occurs is made to depend on some factor in addition to priority class. A lower priority customer is pre-empted if and only if the queue length of higher priority customers is N, a decision parameter. The stochastic model (without priorities) is that of the M/G/1 queue. First moment expressions (e.g., expected number of customers in the system) in the steady state case are obtained for each priority class, using the concept of work conservation. A linear cost model is introduced which is a function of expected waiting time and expected number of pre-emptions. By considering a parametric class of rules determined by the decision parameter, the problem of finding an optimal rule is formulated.

Date: 1971
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