Consider a single-aisle AS/R system, where storage and retrieval requests arrive according to an independent Poisson process at a rate of s  8 storages/hour and r  32 retrievals/

hour. To serve the requests, the S/R machine follows the strategy depicted in Figure 10.46; that is, upon completing a retrieval, it first checks the storage queue, and upon completing a storage, it first checks the retrieval queue, and so on. The I/O point is located at the lower lefthand corner of the rack. System parameters are such that E(SC )  1.3333 minutes, E (TB )  0.4666 minute, and P  D  0.10 minute. Show that the above system is stable (i.e., that it meets the required throughput), and then compute the expected S/R machine utilization.

SECTION 10.7