A queueing inventory system with threshold based priority service and a flexible server

Abstract

In this paper, we analyze two-server queueing - inventory system which consists of two-parallel queues and two category of customers i.e., high and low priority customers. The high priority customer generates demand for an item whereas the low priority customers arrive only for repair (not demanding items). Server 1 offers his service to first queue which involves only high priority customers and server 2 is a flexible server who offers his service to both the queues. When there is no availability of service in both the queues, server 1 will be at idle state whereas server 2 goes on vacation. We find a priority service rule to minimize the loss probability of low priority customers. The low priority customers will be served on threshold-based service such that a threshold L which is placed in the second queue and the service starts only if the number customers in the second queue exceeds the threshold level. The limiting probability distribution of the four random variables is computed in steady state. Also, some significant change in measures of the system are derived. Finally, the suitable cost function is defined and significant numerical examples are projected.