MARKOVIAN INVENTORY MODEL WITH TWO PARALLEL QUEUES, JOCKEYING AND IMPATIENT CUSTOMERS

Abstract

This article presents a perishable stochastic inventory system under continuous review at a service facility consisting of two parallel queues with jockeying. Each server has its own queue, and jockeying among the queues is permitted. The capacity of each queue is of finite size L. The inventory is replenishedaccordingtoan(s,S)inventorypolicyandthereplenishingtimesare assumedtobeexponentiallydistributed. Thelifetimeofeachitemisassumedto beexponential. CustomersarriveaccordingtoaPoissonprocess,andtheyjointhe shortest feasible queue. Moreover, if there is more than one inventory level, and amongthequeues,oneisemptyandintheotherqueue,morethanonecustomer is waiting, then the customer who has to be received after the customer being served in the non-empty queue customer is transformed to the empty queue. This will prevent one server from being idle while the customers are waiting in the other queue. The waiting customer independently reneges the system after anexponentiallydistributedamountoftime. Thejointprobabilitydistributionof the inventory level, the number customers in both the queues and the status of the server is obtained in the steady state. Some important system performance measuresinthesteadystatearederived,andthelong-runtotalexpectedcostrate is also calculated. The results are illustrated numerically.