On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times

Abstract

A generalized queueing system with ( N + 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform. The standard K l / K m /1 queueing system with uniformly bounded sojourn times is considered in particular.