Simulation of semi-Markov processes and Markov chains ordered in level crossing

Abstract

In this paper we address the simulation of stochastic processes ordered in level crossing, where, as proposed by Irle and Gani, X is slower in level crossing than Y if it takes X stochastically longer than Y to exceed any given level. This ordering has immediate applications to the analysis of first-passage times, which are important for detailed performance analysis of distributed computer and communication systems, like the response time of an Internet search-engine query. We provide algorithms for the simulation of level crossing ordered discrete time Markov chains, semi-Markov processes, and continuous time Markov chains under conditions derived recently.