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A distributed algorithm is introduced for the analysis of large continuous time Markov chains (CTMCs) by combining in some sense numerical solution techniques and simulation. CTMCs are described as a set of processes communicating via message passing. The state of a process is described by a probability distribution over a set of reachable states rather than by a single state. Simulation is used to determine event times and messages types to be exchanged, whereas transitions are realized by vector matrix products as in iterative numerical analysis techniques. In this way, the state space explosion of numerical analysis is avoided, but it is still possible to determine more detailed results than with simulation. Parallelization of the algorithm is realized applying a conservative synchronization scheme, which exploits the possibility of precomputing event times as already proposed for parallel simulation of CTMCs. In contrast to a pure simulation approach, the amount of computation is increased, whereas the amount of communication keeps constant. Hence it is possible to achieve even on a workstation cluster a significant speedup.

A distributed numerical/simulative algorithm for the analysis of large continuous time Markov chains