A Survey on the Queueing Inventory Systems with Phase-type Service Distributions

Abstract

Phase-type distributions constitute a very versatile class of distributions. They have been used in a wide range of stochastic modeling applications in areas as diverse as telecommunications, finance, queueing theory, survival analysis, inventory systems. This paper reviews queueing inventory systems (QIS) with phase-type service distributions and discusses their contributions to inventory management. We have classified QIS as features in queueing model such as vacation, service discipline, customer behavior and in inventory model such as review policy, replenishment policy, stock-out assumption. The framework of literature review in this paper clearly provides an overview of the queueing inventory systems and can be used as a starting point for further study.