Markovian queueing inventory system with two stage working vacations

Abstract

This paper studies the behaviour a of two stage working vacations of a single server on Markovian queueing inventory system. The server starts taking two successive working vacations whenever the stock level and the customer level in the queue are both zero. The service rate in the 1st stage working vacation is considered to be lesser than the service rate in regular busy period but greater than the service rate in the 2nd stage working vacation. The nature of the inventory is perishable and the replenishment policy of any order is (s;Q). The steady state joint distribution of the inventory level, the status of the single server and the number of customers in the queue are obtained. Various characteristics of system performance in the steady state are derived and the longrun expected total cost rate is estimated. Several events with numerical examples, which provides the optimal behaviour of the system are presented.