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This research explores analytical models useful in the design of vehicle-based automated material handling systems (AMHS) to support semiconductor manufacturing. The objective is to correctly estimate the throughput and move request delay. The analysis approach is based on queuing network models, but taking into account details of the operation of the AMHS. We analyze the vehicles movement in the system using a Markov chain. This analysis provides the essential parameters such as the blocking probabilities in order to estimate the performance measures. A numerical example is provided to demonstrate and validate the queuing model.