Time Dependent Priority Queues

Considered is a class of rth order delay-dependent priority queuing disciplines in which a customer from the pth priority group, who arrives at time T, has a priority q_p(t) at time t given by q_p(t) = b_p(t − T)^r. The main result states that the expected wait on queue for p-type customers in an rth order system with parameter set [b_p] is identical to the wait in any other such system, say one of order r′ with parameter set [b_p′] if these parameters are chosen in the proper manner. From this, using the results due to Kleinrock for the first order systems, we obtain the expected wait on queue, conditioned on the priority groups, for any rth order system. This class of queuing disciplines ranges from Cobham's fixed priority system (for r → 0) to the first-come-first-served system (for r → ∞). For the case of two priority groups the set {b_p} is chosen so as to minimize a class of delay-dependent cost functions. Results from a computer simulation are given to display the behavior of the waiting time variance.