| We present a scalable hybrid systems modeling framework to describe the flow of traffic in communication networks. To characterize network behavior, these models use averaging to continuously approximate discrete variables such as congestion window and queue size. Because averaging occurs over short time intervals, one still models discrete events such as the occurrence of a drop and the consequent reaction (e.g., congestion control). The proposed hybrid systems modeling framework fills the gap between packet-level and fluid-based models: by averaging discrete variables over a very short time scale (on the order of a round-trip time), our models are able to capture the dynamics of transient phenomena fairly accurately. This provides significant flexibility in modeling various congestion control mechanisms, different queuing policies, multicast transmission, etc. We validate our hybrid modeling framework by comparing simulations of the hybrid models against packet-level simulations. We find that the probability density functions produced by ns-2 and our hybrid model match very closely with an L1-distance. We also present complexity analysis of ns-2 and the hybrid model. These tests indicate that hybrid models are considerably faster. Finally, we provide software tools for the design, analysis, and evaluation of large-scale computer networks and their protocols. |
