On a Queueing System with Processing of Service Items under Vacation and N-policy with Impatient Customers

Abstract

We assume that customers arrive at a single server queueing system according to Markovian Arrival process. When the system is empty, the server goes for vacation and produces inventory for future use during this period. The maximum inventory level permitted is L. The inventory processing time follows phase type distribution. The server returns from vacation when there are N customers in the system. Service time follows two distinct phase type distributions depending on whether the processed item is available or not at service commencement epoch. Customers join the queue with probability p and balk with probability 1-p. Also customers waiting for service become impatient and renege after a random time period which is exponentially distributed. We find the distribution of time until the number of customers hit N. Several system performance characteristics are computed. Also we computed Laplace Stieltjes Transform of the waiting time distribution for the case of no reneging. For the special case of no reneging, some numerical experiments for computing individual optimal strategy, maximum revenue to the server and social optimal strategy are also discussed.