Running out of inventory creates lost sales on one side, and a potential for losing customers on the other. The former is studied in inventory theory, and the latter in queueing theory. This paper combines both inventory management and customer queueing, and presents explicit performance measures for service systems with attached inventories. Many results are presented, including those on optimal policies in classes of feasible policies for minimizing the ratio of queue size to inventory size. In particular, Markovian/Markovian/one (M/M/1) queues with inventories and variants of systems and policies are investigated.

The paper has a traditional mathematical structure, with definitions, theorems, and proofs (some in Appendix B). Researchers in queueing theory are the intended readers. Numerous remarks and examples help readers understand the practical interpretations and ramifications of the results. Additionally, Appendix A expands the discussion with more systems and policies, making this an interesting paper both for researchers and practitioners.