Using partial differential equations to model TCP mice and elephants in large IP networks

Fluid models of IP networks have been recently proposed as a way to break the scalability barrier of traditional discrete state-space models, both simulative (e.g., ns-2) and analytical (e.g., queues and Markov chains). Fluid models adopt an abstract deterministic description of the average network dynamics through a set of ordinary differential equations that are then solved numerically, obtaining estimates of the time-dependent network behavior. However, an important limit of the fluid model approaches presented so far in the literature is their unnatural representation of scenarios comprising the short-lived TCP flows that dominate in today's Internet. In this paper we propose a new fluid model approach in which a different description of the dynamics of traffic sources is adopted, exploiting partial differential equations. This new description of the source dynamics allows the natural representation of short-lived as well as long-lived TCP connections, with little sacrifice in the scalability of the model. In addition, the use of partial differential equations permits the description of distributions, instead of averages, thus providing better accuracy in the results. The comparison between the performance estimates obtained with fluid models and with ns simulations proves the accuracy of the proposed modeling approach.