Multi-server queueing loss models capture important features of real time services. Arriving customers make their decision to join the system based on the availability of resources as well as the current service price. Given a fixed number resources, the manager may then use price as a mechanism to control the utilization of the system. A major objective for the manager is then to find a pricing policy that maximizes total revenue while meeting the quality of service targets desired by the customers.

Using variational calculus techniques, we solve a dynamic optimal control problem by approximating the loss model as a constrained offered load model. We then use customer demand forecasts to anticipate future service congestion and implement a congestion pricing algorithm.

This is joint work with Robert C. Hampshire of Carnegie Mellon University and Qiong Wang of Bell Labs.

A preprint of the paper can be downloaded at Link.