Analysis of Markov chains using simulation graph models

The construction of simulation graph models of Markov chains is demonstrated. This approach enables one to evaluate the chain either numerically through simulation or analytically through path analysis. The user can either directly simulate the associated stochastic process and obtain estimates of the desired measures of performance, or analyze the directed paths in the simulation graph model and analytically compute the probabilities of possible realizations. This method can be used in conjunction with simulation to address such problems as rare event estimation, initialization bias, and determination of initial conditions