Instability and performance limits of distributed simulators of feedforward queueing networks

Reviewer: Mitchell Snyder

The stochastic behavior of input queues in discrete event simulators of feedforward networks is covered in this paper based on Shorey's doctoral dissertation. The authors prove that, under various assumptions that are commonly used in simulators, at least one input queue is unstable. The simulators under investigation work in the following way. Messages arrive at a single processor from different sources. The output of each source is an input queue to the processor. There is an event sequencer between the input queues and the processor whose job it is to guarantee that the messages are processed in correct chronological order. The problem arises when one input queue is empty. The sequencer cannot pass a message from a different input queue to the processor, because it is possible that the next message to arrive in the empty queue has an earlier timestamp than any of the messages that have already arrived. Thus, messages must accumulate in the other queues until a message finally arrives in the empty queue. The main result of the paper is that even if the sequencer is omniscient (“maximum lookahead”), under Poisson and exponential assumptions, at least one of the input queues is a Markov chain that is either transient or null-recurrent. The implication for practitioners is that there must be some sort of synchronization control among the message sources. The paper is long, but very well written. It contains easy-to-understand descriptions of the various models and assumptions, including clear diagrams. The main audience is theoreticians in queueing theory and simulation theory. Practitioners who model networks and write simulators should also be aware of the results.