Light traffic heuristic for an \(M/G/1\) queue with limited inventory (Q689259)

Motivated by solving a stylized location problem, the authors develop a light traffic heuristic for an \(M/G/1\) queue with limited inventory that gives rise to a closed form expression for average delay in terms of basic system parameters. Simulation experiments illustrate the heuristic. The inventory level drops by one unit after each service completion an whenever it drops to a pre-specified level \(u\), an order is placed with replenishment time \(\sim\exp(\gamma)\). Upon replenishment the inventory is restocked to a pre-specified level \(s\) and any arrivals when there is no inventory are placed in queue. Applications to inventory management problems are discussed.