Modeling Communication Networks With Hybrid Systems

This paper introduces a general hybrid systems framework to model the flow of traffic in communication networks. The proposed models use averaging to continuously approximate discrete variables such as congestion window and queue size. Because averaging occurs over short time intervals, discrete events such as the occurrences of a drop and the consequent reaction by congestion control can still be captured. This modeling framework, thus, fills a gap between purely packet-level and fluid-based models, faithfully capturing the dynamics of transient phenomena and yet providing significant flexibility in modeling various congestion control mechanisms, different queueing policies, multicast transmission, etc. The modeling framework is validated by comparing simulations of the hybrid models against packet-level simulations. It is shown that the probability density functions produced by the ns-2 network simulator match closely those obtained with hybrid models. Moreover, a complexity analysis supports the observation that in networks with large per-flow bandwidths, simulations using hybrid models require significantly less computational resources than ns-2 simulations. Tools developed to automate the generation and simulation of hybrid systems models are also presented. Their use is showcased in a study, which simulates TCP flows with different roundtrip times over the Abilene backbone.