Effect of Pricing Intervals on Congestion-Sensitivity of Network Prices

One of the key issues for implementing congestion pricing is the pricing granularity (i.e. pricing interval or time-scale). The Internet traffic is highly variant and hard to control without a mechanism that operates on very low time-scales, i.e. on the order of round-trip-times (RTTs). However, pricing naturally operates on very large time-scales because of human involvement. Moreover, structure of wide-area networks does not allow frequent price updates for many reasons, such as RTTs are very large for some cases. In this paper, we investigate the issue of pricing granularity and identify problems. We first focus on how much level of control over congestion can be achieved by congestion pricing. To represent the level of control over congestion, we use correlation between prices and congestion measures. We develop analytical and statistical models for the correlation. In order to validate the correlation model, we develop packet-based simulation of our congestion pricing scheme Dynamic Capacity Contracting. We then present the fit between simulation results of the pricing scheme and the correlation model. The correlation model reveals that the correlation degrades at most inversely proportional to an increase in the pricing interval. It also reveals that the correlation degrades with an increase in mean or variance of the traffic. Secondly, we discuss implications of the correlation model. According to the model and simulation results, we find that control of congestion by pricing degrades significantly as pricing granularity increases.