Inventory control with two switch-over levels for a class of M/G/1 queueing systems with variable arrival and service rate

This paper deals with inventory control in a class of M/G/1 queueing systems. At each point of time the system can be switched from one of two possible stages to another. The rate of arrival process and the service rate depend on the stage of the system. The cost structure imposed on the model includes both fixed switch-over costs and a holding cost at a general rate depending on the stage of the system. The rule for controlling the inventory is specified by two switch-over levels. Using an embedding approach, we will derive a formula for the long-run average expected costs per unit time of this policy. By an appropriate choice of the cost parameters, we may obtain various operating characteristics for the system amongst which the stationary distribution of the inventory and the average number of switch-overs per unit time.