An $$M/E_{K}/1/N$$ M / E K / 1 / N Queueing-Inventory System with Two Service Rates Based on Queue Lengths

Abstract

The aim of this paper is to investigate a system consisting of a perishable inventory which uses a two-rate service policy following a finite queueing system with a continuous review (s, Q) ordering policy. The service rate is provided to the customers based on the length of the queue. It is assumed that the arrival of a customer into the system follows a Poisson process, the service of an item follows Erlang K phase distribution; the lead time and the life time of an item are both exponentially distributed and balking with the fixed probability is considered. The stationary distribution of the number of customers in the system, server status and the inventory level is obtained by matrix method. The Laplace–Stieltjes transforms of waiting time distribution and nth order moments of waiting time distribution and some important system performance measures in the steady state are derived. Finally, the results of two-rate service policy are illustrated numerically and we studied the convexity of the system which minimizes the total expected cost in the long run.