Fluid-Based Analysis of TCP Flows in a Scale-Free Network

Abstract

In this paper, we derive distributions of throughput, round-trip time, and packet loss probability of TCP flows in a scale-free network. Different from non scale-free networks such as ER (Erdös and Rényi) random graph, the connecting probability between nodes is dependent on their node degrees in scale-free networks. Hence, scale-free networks are generally not easy to analyze. Fekete et al. have derived the average throughput of TCP flows in a scale-free network by limiting network topologies to a class of scale-free trees (i.e., BA (Bárabasi Albert) tree). Not only the average throughput of TCP flows but also distributions of their performance metrics are important for design and control of communication networks. In this paper, we therefore derive distributions of throughput, round-trip time, and packet loss probability of TCP flows in a scale-free network. Similarly to Fekete's approach, we use the BA tree as the network topology. Dynamics of TCP flows and routers are modeled with fluid-flow models. By utilizing known analytical results (i.e., distributions of link betweenness and path length in BA trees), we derive distributions of throughput, round-trip time, and packet loss probability of TCP flows in steady state.

Fluid-Based Analysis for Understanding TCP Performance on Scale-Free Structure

“…In this paper, we clarify the impact by applying the analytic method proposed in Ref. [11]. In the conference paper [26], we presented the short version of this paper.…”

“…In Ref. [11], we proposed an analytic method to derive the probability distributions of the TCP performance on the basis of fluid-based analysis utilizing the probability distributions derived in Refs. [24], [25].…”

“…[24], [25]. In this paper, we discuss the impact of the scale-free structure on the TCP performance using the analytic method proposed in the conference paper [11]. In this paper, we clarify the impact by applying the analytic method proposed in Ref.…”

“…In this paper, we add the explanation of our analysis in detail, and the numerical results for the validation of our analysis. Therefore, this paper is the extension of the conference papers [11], [26].…”

“…We generate scale-free trees with the method [10], which can adjust the strength of the scale-free property by a parameter. In order to clarify statistical characteristic of the TCP performance in the scale-free structure, we focus on TCP flows passing through a bottleneck link in a scale-free tree, and derive the probability distributions of the TCP performance using the analytic method [11] based on fluid-flow approximation of TCP congestion control. Through numerical examples of our analysis, we clarify the im-pact of the scale-free structure on the TCP performance.…”