On the Busy Periods of Single-Server Queues with Poisson Input and General Service Times

We consider a single-server queue with Poisson input and general service times and determine the following probabilities: the probability that a busy period has length ≦ x and the maximal queue size during the busy period is ≦ k, and the probability that a busy period has length ≦ x and the maximal virtual waiting time during the busy period is ≦ y.