Parallel simulation of Markovian queueing networks using adaptive uniformization

This paper describes a method for simulating a large class of queueing network models with Markovian phase-type distributions on parallel architectures. The method, which is based on uniformization, exploits Markovian properties that permit one to first build schedules of simulation times at which processors ought to synchronize, and then simulate a mathematically correct sample path through the pre-chosen schedule. While the technique eliminates many of the overheads incurred by other synchronization methods, it may suffer when the maximum rate (in simulation time) at which one processor might possibly ever send jobs to another is much larger than the average rate at which it actually does. We show how to reduce these overheads, sometimes doubling the execution rate as a result. We discuss experiments performed on the Intel iPSC/2 and Touchstone Delta architectures, where speedups in excess of 155 are observed on 256 processors.