Parametric Priority Rules: An Approach to Optimization in Priority Queues

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.