The M=M=1 Queue with Single Working Vacation Serving at a Slower Rate during the Start-up Period

Abstract

We consider the M/M/1 queue with single working vacation serving at a slower rate during the start-up period. In order to save energy and reduce waste, the server works at a slower rate rather than completely stops during a vacation and start-up period. Using quasi birth and death process and matrix-geometric solution method, we obtain the distribution of the nember of customers in the system, the average nember of the customers and the average sojourn time of a customer in the stationary state.