A new admission control scheme in queueing-inventory system with two priority classes of demands

Queueing-inventory system (QIS) plays an important role in practice. Here, such a system with two types of demands needing servicing with inventory items is studied. Both the demands share a common waiting space if the services cannot be offered immediately. We look at both finite and infinite waiting spaces. While Type 2 demands are admitted as long as the requirement of at least one waiting space and at least one inventory is met; however, Type 1 demands are admitted under an admission control scheme involving a threshold. Under the assumptions of an all-around point process to describe the demands, exponential processing and exponential replenishment times, and with an \((s, S)-\) $(s,S)-$ type inventory policy, we analyze the QIS. Representative numerical examples are discussed.