Queues with M/G/∞ input: A survey and some new results

As input traffic at various nodes in packet switched telecommunication networks typically exhibits considerable correlation, there is a continuing interest in queuing systems with correlated arrivals. The class of M/G/∞ arrival models can account for various types of arrival correlation, has a two-level structure which is appealing in the context of network protocol stacks, and is characterised by only few parameters. Moreover, queues with M/G/∞ input prove to be amenable for a classic queuing analysis. In view of these characteristics, it is not surprising that these models have attracted considerable attention in the past. In this paper, we survey the literature on M/G/∞ type queuing systems, present some new results on these systems, and extend the class of M/G/∞ input models, while retaining the analytic tractability of the corresponding queuing systems.