Packet models revisited: tandem and priority systems

We examine two extensions of traditional single-node packet-scale queueing models: tandem networks and (strict) priority systems. Two generic input processes are considered: periodic and Poisson arrivals. For the two-node tandem, an exact expression is derived for the joint distribution of the total queue length, and the queue length of the first queue, implicitly determining the distribution of the second queue. Similarly we derive the distribution of the low-priority queue in a two-class priority system. We also provide explicit approximations based on the Brownian bridge.