To compute the expected travel time of storage and retrieval (S/R) machine in automated warehousing systems most of the previous studies assumed that equal number of rack openings are required regardless of the nature of storage assignment rules. It is known that randomized storage assignment rule usually needs less storage to space than needed for full turnover-based assignment rule. The objective of this paper is compute the expected travel time of each assignment rule more equitably by taking into account the storage space required for each rule. First, the rack storage space is determined which satisfies a given service level. Then based on the standard Economic Ordering Quantity model, trade-off analysis is carried out which relates the storage space to the expected travel time of the S/R machine. Finally, example problems are solved to compare the performance of each assignment rule under varying conditions of demand pattern and service level.