A computationally effective analysis of the throughput performance of a closed-loop multi-vehicle automated material handling system (AMHS) used in highly automated 300 mm wafer fabrication facilities (fabs) is presented. A probabilistic model is developed, based on a detailed description of AMHS operations, and the system is analyzed as an extended Markov chain. The model represents vehicle operations on the closed-loop considering the possibility of vehicle blocking. This analysis provides essential parameters such as the vehicle blocking probabilities and the throughput capacity of the AMHS. A numerical example is analyzed and simulated using AutoMod to demonstrate and validate the stochastic model.