Exact Simulation for Fork-Join Networks with Heterogeneous Service

This paper considers a fork-join network with a group of heterogeneous servers in each service station, e.g. servers having different service rate. The main research interests are the properties of such fork-join networks in equilibrium, such as distributions of response times, maximum queue lengths and load carried by servers. This paper uses exact Monte-Carlo simulation methods to estimate the characteristics of heterogeneous fork-join networks in equilibrium, for which no explicit formulas are available. The algorithm developed is based on coupling from the past. The efficiency of the sampling algorithm is shown theoretically and via simulation.