Algorithms for the State Probabilities in a General Class of Single Server Queueing Systems with Group Arrivals

Single server queues with batch arrivals are useful in the modeling of computer and communication systems amongst others. In this paper we give for a wide class of single server queues with batch arrivals a stable recursive method to compute state probabilities both at arrival and at arbitrary epochs. This class includes finite capacity models with state dependent Markovian input in which batches could be totally or partially rejected. The customers of a batch are served individually and the service time has a general distribution function. In particular, we discuss as application the computation of operating characteristics, such as rejection probability and probability of server idleness, for a finite capacity M/G/1 queue for which arriving customers are rejected if their waiting plus service times exceed the capacity of the system.