Linear retrial inventory system with second optional service under mixed priority service

Abstract

The present paper deals with a generalization of the homogeneous single server finite source retrial inventory system with two classes of customers - one with high priority customer and the other with low priority customer. The inventory is replenished according to an (s, Q) policy and the replenishing times are assumed to be exponentially distributed. The server provides two types of services - one with essential service and the other with a second optional service. The service times of the 1st (essential) and 2nd (optional) services are independent and exponentially distributed. The high priority customers have a mixed priority over the low priority customers. Retrial is introduced for low priority customers only. The joint probability distribution of the number of customers in the waiting hall, 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 and the long-run total expected cost rate is also derived.