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

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.