Scale functions of levy processes and busy periods of finite-capacity M/GI/1 queues

Abstract

In this paper we use the exit time theory for Levy processes to derive new closed-form results for the busy period distribution of finite-capacity fluid M/G/1 queues. Based on this result, we then obtain the busy period distribution for finite-capacity queues with on-off inputs when the off times are exponentially distributed. © Applied Probability Trust 2004.