The effect of bandwidth and buffer pricing on resource allocation and QoS

Congestion-based pricing of network resources is a common approach in evolving network architectures that support Quality of Service (QoS). Resource usage and QoS will thus fluctuate in response to changes in price, which must be dynamically controlled through feedback. Such feedback algorithms typically assume that network resources behave as Normal goods, i.e. that an increase in the price of a resource results in a decreased demand for that resource. Here, we investigate the sensitivity of resource allocation and the resulting QoS to resource prices in a reservation-based QoS architecture that provides guaranteed bounds on packet loss and end-to-end delay for real-time applications. We derive necessary and sufficient conditions for bandwidth and buffer to act as Normal goods, showing that this depends on the shapes of the utility and QoS functions. We then show that the minimum total cost is a decreasing convex function of loss. When the delay constraints are absent or not binding, we prove that if a resource is a Normal good, then an increase in the price of that resource causes the loss on that link to increase, the loss on all other links to decrease, and the total loss to increase. We also give sufficient conditions to establish that an increase in the price for a resource results in a decreased demand for that resource, an increased demand for the other resource at that node, and an increased demand for resources at all other hops. Finally, when the delay constraint is binding, we give sufficient conditions to establish that an increase in the price of bandwidth at one node results in increased loss and delay at that node, and decreased loss and delay at all other nodes.