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A computationally efficient cycle time model for conceptualizing autonomous vehicle storage and retrieval systems and comparing their performance with crane-based automated storage and retrieval systems is presented. The model is based on an iterative computational scheme exploiting random storage assumptions and queuing model approximations. Relative to earlier models, the procedure scales up efficiently for large problems thereby enabling more extensive search of a design solution space. Simulation based validation studies suggest that model accuracy is adequate for system conceptualization. The procedure is demonstrated using realistically sized sample problems.