Numerical investigation on MAP/PH(1), PH(2)/2 inventory system with multiple server vacations

In this paper, we consider an inventory system with two heterogeneous servers and multiple vacations. We have assumed that the customers arrive according to a Markovian arrival process and two parallel servers who provide heterogeneous phase type services to customers. The inventory is replenished according to an (s, S) policy and the replenishing time is assumed to follow exponential distribution. The vacation times of both severs are assumed to be independent and identically distributed exponential random variables. The joint probability distribution of the number of customers in the system, inventory level and server status is obtained in the steady state. Some important performance measures are obtained and the optimality of an expected total cost rate is shown through numerical illustration.