Simulation Methodologies for Transient Markov Processes: A Comparative Study Based on Multi-Echelon Repairable Item Inventory Systems

摘要

Consider Monte Carlo simulation of transient behavior of continuous time Markov processes with large finite state spaces. The usual event-scheduling approach is compared to four alternative approaches which do not use event lists. Variance reduction, programming effort, and storage requirements are considered. All Monte Carlo simulation programs are written in SIMSCRIPT II.5. These approaches are then compared to a deterministic method called Randomization. The four alternative Monte Carlo simulation methods are based on two dichotomies. The first concerns continuous versus discrete time; the process can be simulated directly in continuous time or the uniformized embedded discrete time Markov chain can be simulated and then analytically randomized to recover the original continuous time process. The second dichotomy concerns a table look up versus an algorithmic approach: the mean holding time and the transition distribution for the current state of the simulated process can be read from memory (requiring large memory storage) or computed (requiring more computation time).