Loss probabilities in batch-arrival bulk-service queues with finite capacity

Buffer overflow is important to communication and production systems. For the case where batches arrive according to a Poisson process and the service is in batches that are geometrically distributed, we describe a method to find the exact loss probability. We also give an asymptotic approximation for the loss probability. Numerical experiments indicate that the buffer sizes needed to keep the loss probabilities below a specified level increase when the expected service batch size increases while the offered load is kept constant