Applied Mathematics & Information Sciences

Author Country (or Countries)

South Africa


This article presents a stochastic inventory system under continuous review at a service facility consisting of a finite waiting room and a single server, in which two types of customers arrive in Poisson processes with arrival rates l1 for high priority and l2 for low priority customers. The low priority customers arrive only for repair. The inventory is replenished according to an (s, S) policy and the replenishing times are assumed to be exponential. The service times follow exponential distributions with parameters m1 and m2 for high and low priority customers respectively. Retrial and impatience are introduced for low priority customers only. The orbiting customers independently renege the system after an exponentially distributed time with parameter a > 0. The orbiting customers compete for service by sending signals that are exponentially distributed. The joint probability distribution of the number of customers in the waiting area, the number of customers in the orbit and the inventory level is obtained for the steady state case. Some important system performance measures in the steady state are derived. Several numerical examples are presented to illustrate the effect of the system parameters and costs on these measures.