Tail distribution of the delay in a general batch-service queueing model

Batch servers are capable of processing batches of packets instead of individual packets. Although batch-service queueing models have been studied extensively during the past decades, the focus was mainly put on calculating performance measures related to the buffer content, whereas less attention has been paid to the packet delay. In this paper, we focus on the tail probabilities of the delay that a random packet experiences in a general batch-service queueing model. More specifically, we establish approximations for these probabilities, which are highly accurate and easy to calculate. These results, for instance, allow to accurately assess the probability that real-time packets experience an excessive delay in practical telecommunication systems.