Multilevel Queues with Extremal Priorities

Abstract

This paper deals with a single server serving N priority classes ( N being finite or infinite) and working under an FB z regime, namely, one in which the waiting line consists of infinitely many separate queues obeying the FIFO rule. Each priority class is assigned to one of the queues. A customer from the k th priority class (“ k -customer”) in the n th queue is eligible for θ n,k time units of service, at the end of which he either departs, because his requirement is satisfied, or joins the tail of the ( n + 1)-th queue. When a quantum of service is completed, the server turns to the first customer in the lowest index (highest priority) nonempty queue. The arrival process of k -customers is assumed to be homogeneous Poisson, and their service requirements are independent, generally distributed, random variable. A set of recursive linear equations is derived for the expected flow time of a k -customer whose service requirement is known, and some examples are discussed and presented graphically. This paper corrects some errors in an earlier paper by the second author.