A single server M/G/1 queue with preemptive repeat priority service with server vacation

Abstract

This paper pertains to the study of a Stochastic queueing model with preemptive repeat priority service discipline which plays a prominent role in real life situation like communication network where priority is given important when urgent message is to be communicated, man power planning where the recruitment process following preemptive repeat priority service discipline, VIP’s vehicle during peak hours etc. Here an M/G/1 queue with optional server vacation based on Bernoulli schedule with single server providing two types of service – High priority service (Type I) with probability 1 p and low priority service (Type II) with probability 2 p with service time following general distribution. Further it is assume that the low priority service will be interrupted when a high priority customer arrives in the system. The time dependent probability generating function have been obtained in terms of their Laplace transform and the corresponding steady state results are obtained explicitly for this model. Also some performance measures such as mean queue length and mean waiting time are computed for high priority and low priority queue. The validity of this model is highlighted by means of a hypothetical situation. 4652 S. Baskar and S. Palaniammal Mathematics subject classification: 60K25, 60K30,91B22