Transient analysis of an M/M/c queue subject to multiple exponential vacation

Abstract

In this paper, we consider an M/M/c queueing model subject to multiple exponential vacation wherein arrivals occur according to a Poisson distribution and the c servers provide service according to an exponential distribution. When the system is empty, all the c servers go on a vacation and the vacation times are assumed to follow exponential distribution. Further arrivals are allowed to join the queue when servers are in vacation. Explicit analytical expressions for the time dependent probabilities of the number in the system are presented using matrix geometric method.