Time-segmentation parallel simulation of networks of queues with loss or communication blocking

Abstract

This article is concerned with the efficient simulation of communication systems on parallel processors. In most of the article, we assume that the communication system under study can be modeled as a system of finite exponential queues with a general topology (in particular, the system need not be acyclic) and with either loss or communication blocking. We also assume that to estimate the performance measures of interest, it is necessary to generate long sample paths of the system. This is the case in both steady-state simulations and in long transient simulations. The approach involves applying each processor to simulate the entire system for a part of the time horizon of interest. We present theory guaranteeing the validity of the proposed approach, and numerical results proving the viability of the approach. The proof of the validity of the approach uses the fact that the queueing systems considered are continuous time Markov chains. An essential part of the argument is a proof that sample paths starting from different initial states eventually will couple (i.e., become identical), and a simple method for recognizing the time when a sample path has become independent of the original starting state (i.e., when all sample paths have coupled, regardless of the initial state). Finally, we discuss how our approach can be used for parallel trace-driven simulations of certain nonMarkovian systems, and state the implications of this research for the initialization bias problem in steady-state simulation.