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This paper proposes a queueing-based analytical model useful in the design of closed-loop conveyor-based automated material handling system (AMHS), which has been identified as an effective material handling alternative in next-generation semiconductor wafer fabrication facilities. The model presented in this paper represents practical hardware considerations of the AMHS, such as turntables and crossovers. The objective is to accurately estimate the expected work-in-process (WIP) on the conveyor, queueing delays due to congestion at intersection points, as well as assessing the conveyor system stability. A four-phase approach is used to estimate the WIP. The proposed model is applied to the SEMATECH virtual 300 mm wafer fab. Experimental results demonstrate that in the worst case where the maximum number of crossovers is used and the traffic on the conveyor is high, the analytical model performs very well with average relative errors of 4.2%.