Effect of Pricing Intervals on the Congestion-Sensitivity of Network Service Prices

Abstract— Congestion-sensitive pricing schemes for wide area networks have attracted significant attention over the last decade. Several proposals have been made for congestion-sensitive pricing of the Internet. One key implementation obstacle for these dynamic pricing schemes is the necessity of frequent price updates whereas the structure of wide area networks does not allow frequent price updates since round-trip-times are very large for some cases. As the networks allow infrequent price updates, more control is achieved by the pricing schemes with more frequent price updates. So an important issue to investigate is to find a maximum value for the interval (i.e. pricing interval) over which price updates occur, such that the level of congestion control can remain in a desired range. This paper presents our modeling and analysis work for the length of pricing intervals. To represent the level of control over congestion, we use correlation between prices and congestion measures. After developing an approximate model for the correlation, we find and prove that the correlation degrades at most inversely proportional to an increase in the pricing interval. We also find that the correlation degrades with an increase in mean or variance of the incoming traffic. Keywords— Network Pricing, Congestion-Sensitive Pricing, Congestion Control, Quality-of-Service