Busy periods in time-dependent M/G/1 queues

Abstract

A single-server queue with batch arrivals in a non-homogeneous Poisson process and with balking is studied with respect to the busy period, using supplementary variables. A system of integral equations is obtained on the base of which the transforms are expressed in series. For the homogeneous case, assuming finite waiting room, the solutions are obtained via Cramer's rule. This gives asymptotic expressions for the expectations for large arrival intensity. An efficiency measure giving the long run loss probability is given. For a special case contour integral representations are given as solutions.