Sensitivity of optimal quality of service to bandwidth and buffer prices

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. Here, we investigate the sensitivity of QoS to resource prices in a reservation-based QoS architecture. Such sensitivities are crucial to guide development of price adjustment algorithms. We derive necessary and sufficient conditions for resources to act as normal goods. We then show that the minimum total cost is a decreasing convex function of loss. Finally, 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.