Waiting time and other first-passage time measures in an (s,S)(s,S) inventory system with repeated attempts and finite retrial group

In this paper we consider a continuous review inventory system in which unsatisfied demands, due to lack of stock, are sent to a pool and are repeated until being satisfied. The inventory is replenished according to an (s,S)(s,S) policy and the replenishment times follow an exponential distribution. We concentrate on performance measures related to the waiting time and first-passage times of the system. More concretely, we study the waiting time of a demand, the time between replenishment orders and the orbit idle time or interval without pending demands. Several numerical examples are presented to illustrate the effect of the system parameters on these measures.