Queue Length Dependent Priority Queues

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.