A Single Server Queueing System Working under Mixed Priority Disciplines

A single server dispenses service to m priority classes of customers. The arrival process of the i th class, i = 1, 2, …, m , is a homogeneous Poisson distribution. Service times of each class are independent identical arbitrarily distributed random variables with a finite second moment. The smaller the index of a class, the higher its priority degree. For i j , class i has preemptive priority over j if and only if (iff) j − i > d , and nonpreemptive priority otherwise, where d is a predetermined non-negative integer. Within each priority class the FIFO service rule is obeyed. Setup activities take place before starting or resuming service. An interrupted service is resumed when the system contains no customers with preemptive priority. The preemptive regimes considered are resume and repeat with and without resampling. For each of the mixed disciplines the steady state Laplace-Stieltjes transforms and the expectations of the waiting time and the time in the system are calculated for a k customer ( k = 1, 2, …, m ). Guidelines for minimization of the system's expected operating cost per unit time with respect to d and to the priority assignment, are discussed. Results are illustrated by a numerical example.