Pricing and distributed QoS control for elastic network traffic

Web measurements have shown that TCP flow sizes vary over several orders of magnitude. If network resources are shared fairly, the performance of short TCP flows is seriously degraded by long flows. This motivates prioritization of short over long flows, leading to significant performance improvement for short flows, with very little degradation for long ones. By imposing an appropriate pricing structure, users can be provided with incentives so as to enforce such a prioritization in a distributed manner. We study the situation where users randomly generate elastic flows (according to a Poisson process), whose sizes have a general probability distribution. Users may choose between two service classes that share the available resources with preemptive priority for one class. We assume fair sharing within each class and use a processor-sharing model with two priority classes to evaluate flow transmission times. For given price functions, users choose the service that best fits their profile, or refrain from service (`balk') if the prices exceed the willingness to pay for both services. We show that under mild modeling assumptions, the revenue maximizing Nash equilibrium is such that short flows opt for the premium service and long flows for the low-priority service. It is optimal for medium-sized flows to balk when the offered load is relatively high. Although this allocation is the result of distributed control, aside from the flows that balk, it accomplishes precisely the prioritization of short flows which improves overall performance as mentioned above