Waiting Time in an (S − 1, S) Inventory System

Steady-state distribution functions are derived for waiting time in an (S − 1, S) inventory system in which arrivals are governed by members of the geometric Poisson family, resupply times are independently and identically distributed negative exponential variates, and service is on a first-come-first-served basis. For small values of S, probabilities can be computed readily from the final forms of the distribution functions using gamma and exponential function tables.