Impatient Customer Queue with Single Working Vacation

Abstract

This paper analyzes an infinite buffer M/M/1 queue with single working vacation in which customers arrive according to a Poisson process. As soon as the system becomes empty, the server takes working vacation. The service rate during regular busy period, working vacation period and vacation times are assumed to be exponentially distributed. During working vacation customers may renege due to impatience and the impatient timer follows exponential distribution. The steady-state probabilities and performance measures are obtained by using probability generating function. Various numerical results are presented to show the effect of the some parameters on the system performance measures.