An Invariance in the Priority Queue with Generalized Server Vacations and Structured Batch Arrivals

Abstract Shanthikumar (Shanthikumar, J.G. Level crossing analysis of priority queues and a conservation identity for vacation models. Nav. Res. Log. 1989, 36, 797–806) studied the priority M/G/1 queue with server vacations and found that the difference between the waiting time distribution under the non‐preemptive priority (NPP) and that under the preemptive‐resume priority (PRP) is independent of the vacation policy. We extend this interesting property: (i) to the generalized vacations which includes the two vacation policies considered by Shanthikumar; (ii) to the structured batch Poisson arrival process; and (iii) to the discrete‐time queues.