On the longest service time in a busy period of the M⧸G⧸1 queue

This paper considers the supremum m of the service times of the customers served in a busy period of the M?G?1 queueing system. An implicit expression for the distribution m(w) of m is derived. This expression leads to some bounds for m(w), while it can also be used to obtain numerical results. The tail behaviour of m(w) is investigated, too. The results are particularly useful in the analysis of a class of tandem queueing systems.