Stability of queueing-inventory systems with customers of different priorities

We study a production-inventory system with two customer classes with different priorities which are admitted to the system following a flexible admission control scheme. The inventory management is according to a base stock policy and arriving demand which finds the inventory depleted is lost (lost sales). We analyse the global balance equations of the associated Markov process and derive structural properties of the steady state distribution which provide insights into the equilibrium behaviour of the system. We derive a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion. For a special case we show that the condition is necessary as well.

Automated summary

In this study, we investigate a production-inventory system that involves two customer classes with different priorities. These customers are admitted to the system based on a flexible admission control scheme. The inventory management follows a base stock policy, and any arriving demand that results in depleted inventory is considered as lost sales. By analyzing the global balance equations of the associated Markov process, we derive structural properties of the steady state distribution, which provide insights into the equilibrium behavior of the system. We also establish a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion, and show its necessity for a special case.