$1$ An AS$/$RS is being designed; randomized storage is to be used. One alternative being considered is to have each aisle be $70$ tall and $310$ long. The S$/$R has a horizontal speed of $425$ fpm and a vertical speed of $80$ fpm$.$ It requires $0\mathrm{.}40$ minute to pick up or deposit a load. The activity level for the system varies during each shift. The heaviest operating period is a time during which a large number of retrievals must be performed. During peak activity, each S$/$R must be capable of performing $30$ retrievals per hour and $10$ storages per hour. It is expected that $100\%$ of the storages will be performed with dual$-$command cycles