Steady state performance measures of an M/M/1 queue with single working vacation subject to catastrophe

Abstract

A single server queue with Poisson arrival and exponential service times subject to a policy of single working vacation, close down period and catastrophe is considered. The service times are different for the active phase and the working vacation phase. A catastrophe is assumed to occur when there are customers in the system and wipes out the entire system resulting in the system being inactive for a random period of time. Explicit expressions for the steady state probabilities of the close down period, maintenance state and system size for active phase and working vacation phase have been obtained. The effects of various parameters on the system performance measures are studied using numerical examples.