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Parametric Priority Rules: An Approach to Optimization in Priority Queues
K. R. Balachandran
Vol. 18, No. 3 (May - Jun., 1970), pp. 526-540
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/168343
Page Count: 15
You can always find the topics here!Topics: Customers, Cost functions, Unit costs, Cost efficiency, Carrying costs, Cost minimization condition, Operating costs, Random variables, Variable costs, Sufficient conditions
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This paper analyzes priority rules that are mixtures of preemption and postponable rules. Whether a preemption occurs is made to depend on some factor in addition to priority class; dependence on the completed portion of service (age) of the lower-priority customer in service and the number of prior preemptions of the lower-priority customer in service are each considered. The stochastic model (without priorities) is that of the M/G/1 queue. The paper obtains first-moment expressions (e.g., expected number of customers in the system) in the steady-state case for each priority class as a function of the particular factor being considered. It then introduces a linear cost model that is a function of expected waiting time and expected number of preemptions, and formulates the problem of finding an optimal rule from each class by considering a parametric class of rules determined by each factor. In each case, conditions are sought for the global optimality of a rule over a class of rules, but results are obtained only after restrictions (e.g., monotone failure rates) on service distributions are imposed.
Operations Research © 1970 INFORMS