On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivals

Abstract

We consider a single server queueing system M/G/1 in which customers arrive in a Poisson process with meanλt, and the service time has distributiondB(t), 0 <t< ∞. LetW(t) be the virtual waiting time process, i.e., the time that a potential customer arriving at the queueing system at timetwould have to wait before beginning his service. We also let the random variabledenote the first busy period initiated by a waiting timeuat timet= 0.