Stability of queueing-inventory systems with customers of different priorities

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