16. A Stochastic Programming Model for Network Resource Utilization in the Presence of Multiclass Demand Uncertainty

There are numerous applications in which revenues are generated by the use of resources that are distributed over a network. In some cases, these networks are spatial, while in others they are temporal. Nodes in a spatial network, such as those in air transportation and telecommunications industries, correspond to locations on the network, and arcs correspond to the ability to transport goods or provide services between nodes. On the other hand, temporal networks are formed by discretizing time and are commonly used for yield management models for automobile rental companies, hotels, etc. In these models, nodes are often associated with points in time, and arcs correspond to bookings over time. In either case, it is important to recognize that demand is often served by using resources associated with multiple arcs of the network. Airline customers may use multiple flights to complete their itineraries, calls may be routed across multiple links in a telecommunication network, and rental car and hotel customers may retain facilities for multiple days. Furthermore, these networks typically serve multiple classes of customers, some of whom pay higher rates than others. For example, if a television network has a “breaking’’ story for which video conferencing is necessary immediately, they may be willing to pay at a higher rate than a university that has paid in advance to transmit lectures over the same network. Similarly, customers in the airline industry are categorized by fare classes, as are hotel and car rental customers. In any of these applications, the revenue generated by the network depends, in large measure, on the admission control policy used for network management. Intuitively, good control policies will result in a system that serves as many high-paying customers as possible, while maintaining a high level of resource utilization. This paper introduces models that may be used to facilitate the efficient management