A new approach combining simulation and randomization for the analysis of large continuous time Markov chains

Abstract

A new analysis method for continuous time Markov chains is introduced. The method combines, in some sense, simulation and numerical techniques for the analysis of large Markov chains. The basis of the new method is the description of a continuous-time Markov chain as a set of communicating processes. The state of all or some of the processes is described by a state vector, including a probability distribution over the set of locally reachable states. Simulation is used to determine the event times and message types exchanged between processes. Local transitions are realized by vector matrix products describing the next state distribution form the current one. In this way, the state explosion problem of numerical analysis is avoided, but it is still possible to obtain more accurate results that with pure simulation. The approach is therefore especially useful for the analysis of quantities with small probabilities or for the analysis of rare events.