On a Queueing-Inventory Model with Age-Based Selling of Items to Distinct Priority Groups

This study focuses on a queueing-inventory system with items having PH-distributed common lifetime and customers of distinct classes arriving according to marked Markovian arrival process. Customers have access permission (priority) to the inventory according to their class number and freshness of the inventory items. Different single-server nodes with (class-dependent) exponential service rates are allotted for each class of customers. The inventory is managed according to (s, S) policy with positive lead time. The system demands reorder when the inventory level reaches s or when the lifetime reaches a particular stage. We model the system as a QBD, and using the matrix-analytic method, the stability condition and steady-state probabilities are obtained. Some vital performance measures are provided, and a cost function is considered for computing the optimal value of reorder points.