Fast Evaluation of Ensemble Transients of Large IP Networks

We extend a numerical approximate solution method (the Z-iteration) to time-dependent open networks of M(t)/M(t)/1/1 and M(t)/M(t)/1/K queues, and apply the method to obtain transient performance metrics of large IP networks. The method generates a set of coupled differential equations, one for each queue in the network. The equations are numerically unstable under certain conditions (e.g., large bandwidths and buffers), and we present techniques to overcome this problem. The resulting numerical procedure is accurate and very fast. For example, a 20-second evolution for a 1000-node network with high-speed links (ß 10 4 packets/sec) and large buffers (ß 10 4 packets) was obtained in 18 minutes on an Ultra Sparc, whereas simulation would take days. 1 Introduction Evaluating the performance of large IP networks is an important problem, but an adequate technique does not currently exist. Analytical approaches cannot handle many critical network features. Packet-level simulation is po..