Simplification of network dynamics in large systems

We show that significant simplicity can be exploited for pricing-based control of large networks. We first consider a general loss network with Poisson arrivals and arbitrary holding time distributions. In dynamic pricing schemes, the network provider can charge different prices to the user according to the current utilization level of the network and other factors. We show that, when the system becomes large, the performance (in terms of expected revenue) of an appropriately chosen static pricing scheme, whose price is independent of the current network utilization, approaches that of the optimal dynamic pricing scheme. Further, we show that, under certain conditions, this static price is independent of the route the flows take. This indicates that we can use the static scheme, with its much simpler structure, to control large communication networks. We then extend the result to the case of dynamic routing, and show that the performance of an appropriately chosen static pricing scheme, with bifurcation probability determined by average parameters, can also approach that of the optimal dynamic routing scheme when the system is large. Finally, we study the control of elastic flows and show that there exist schemes with static parameters whose performance can approach that of the optimal dynamic resource allocation scheme (in the large system limit). We also identify the applications of our results to QoS routing and rate control for real-time streaming.