Instability and performance limits of distributed simulators of feedforward queueing networks

In this article we study the performance of distributed simulation of open feedforward queueing networks, by analyzing queueing models of message flows in distributed discrete event simulators. We view each logical process in a distributed simulation as comprising a message sequencer with associated message queues, followed aby an event processor. We introduce the idealized, but analytically useful, comcept of maximum lookahead. We show that, with quite general stochatstic assumptions for message arrival and time-stamp processes, the meassage queues are unstable for conservative sequencing, and for conservative sequencing with maximum lookahead and hence for optimistic resequencing, and for any resequenceing algorithm that does not employ interprocessor flow control . Finally, we provide formulas for the throughput of distributed simulators of feedforward queueing networks.