Frequency Domain Filter Design and Analysis of Request Scheduling in Internet Servers

Internet traffic has a characteristic of strong correlation. This traffic characteristic greatly complicates the problem of server performance modeling and optimization. Conventional time domain analysis has limitations in the study of the impact of complex traffic on server performance, because self-similarity of Internet traffic is often characterized in frequency domain. In this paper, we present a frequency domain filter model to characterize the relationship between server capacity, resource allocation, and service quality for general input traffic. Power spectral density (PSD) shows the strength of variations (power) as a function of frequency. By the model, server scheduler operates as a filter of input traffic that transforms its PSD function into another PSD function of server utilization process. The optimality of the scheduler in second-order statistics is to minimize the power leakage in the transformation. Most Internet traffic has monotonically decreasing PSD functions. For this type of input traffic, we prove that the optimal schedulers have a convex structure. Uniform allocation is an extreme case of the convexity and is proven to be optimal for traffic of independent arrivals. We integrate the convex-structured scheduling principle with GPS discipline and show that the enhanced GPS policy improves the service quality significantly.