Analysis of a Non-preemptive Priority Queueing-Inventory System with Common Life Time and Cancellation

A queueing-inventory system with cancellation, common life time and non-preemptive priority is considered, in which customer arrives according to a Poisson process and service time follows an exponentially distribution. By formulating the system process into a level-dependent quasi-birth-and-death process (LDQBD), the stability condition and steady-state probability vectors under Neuts-Rao truncation method are obtained. Some performance measures and expected cost function are also given. Then, the optimal maximum inventory level and minimum cost are achieved through numerical simulations. Finally, the sensitivities analysis on major parameters are performed to provide more managerial insights.