On the transient waiting times for a GI/M/1 priority queue

Abstract

In this paper we consider the GI/M/1 queueing model with infinite waiting-room capacity. The customer arriving at t = 0 will find k — 1 customers waiting. The latter customers belong to a second priority class, whereas the ones arriving in [0,∞) belong to a first priority class and have the higher priority. Within each class we have a first-in-first-out queueing discipline. A customer, once at the service-point, remains there until his service is completed. Then the next customer for service is the one of highest priority among those queueing.For this model we derive the transient waiting times for customers belonging to both priority classes. The results are of special interest in appointment systems where customers may not turn up.