Queueing System M/M/1/∞ with Perishable Inventory and Repeated Customers

Abstract

We propose a model of a queueing system with a single server, perishable inventory and repeated customers that can form an orbit of infinite size. In the absence of inventory in the system, primary customers according to the Bernoulli scheme either enter the queue or go into the orbit. The system uses the (s, S)-policy of replenishing the inventory. We develop a method for calculating system characteristics and solve the problem of minimizing total costs by choosing the critical level of inventory.