Markovian two server single vacation queue with balking and heterogeneous service rates

Abstract

In this paper, we consider a queue with two heterogeneous server. In which, the servers takes a single vacation, if there are no customers in the system at a service completion point. The negative exponential distributions follows to the inter-arrival time and the service times. Every arrival of customer requires accurately single server for its service. The customers choose the servers on random selection basis, here the queue discipline is FCFS. The vacation period follows negative exponential distribution. In addition an arriving customer who finds the servers are on vacation, may balk with probability 1−β or may join with probability β. The steady state results have been obtained to this model. Some performance measure and some numerical models are obtained.