A Dynamic Priority Queue with General Concave Priority Functions

Abstract

This paper analyzes mathematically a queueing model where a single server dispenses service to several, m, non-preemptive priority classes. It is assumed that the arrival process of customers who belong to the k class (k customers) is Poisson, and their service times are independent, identical, arbitrarily distributed random variables. The priority degree of a customer at a certain moment is not only a function of his class, but is also a general concave function of the time he has already spent in the system. (The discipline is termed “dynamic-priority.”) Upon departure the server selects for service, from the customers present, the one with the highest instantaneous priority degree, breaking ties by the FIFO rule. An implicit function as well as upper and lower bounds on the expected waiting time of k customer are found. The effectiveness of the bounds is demonstrated by a numerical example.