Dependence in Packet Queues, I: A Multi-Class Batch-Poisson Model.

Packet communication networks such as the AT&T Communications Packet Transport Network (PTN) carry several classes of traffic, each with its own service characteristics, e.g., packetized voice, short data messages, bulk data (files), facsimile, acknowledgements and other signals. The packet arrival processes from each source are also often bursty (highly variable), which can contribute to long packet delays. This burstiness has been previously characterized in packet network performance models by the dependence among successive interarrival times. Here it is shown that associated dependence among successive service times and between service times and interarrival times also can be important. In this memorandum, these dependence effects are demonstrated analytically by considering a multi-class single-server queue with batch-Poisson arrival processes.