Queues with batch poisson arrivals and hyper‐exponential service

Abstract

Abstract We consider in this paper the queueing system in which the input is in batches of variable numbers following a Poisson distribution; queue discipline is “first come first served,” it being assumed that the batches are preordered for service purposes; and service time distribution is hyperexponential with n branches. The Laplace transform of the system size distribution is determined by applying the method of generating functions, devised by Bailey [1] . Some of the known results are derived as particular cases.