Semi-Markov processes as models for telecommunications systems with heavy-tailed traffic

Date of Completion

January 2005


Computer Science




Innumerable studies over the past few years have provided ample empirical evidence that Internet traffic is self-similar, highly varying and bursty over a wide range of time scales. Such traffic is also characterized by long-range dependent properties that bear negative implications on various network performance measures, such as router delay and packet loss probability. The statistical realm, where self-similarity is well understood, lacks the mechanisms to represent the host behavior and system properties that underlie self-similarity, and is therefore limited in its suitability to provide insights for network engineering. Other research efforts have adopted a structural approach to the problem, aiming to capture the physicality of network mechanisms through Markovian models. As such, research in analytical models of self-similar traffic has provided important results that characterize traffic burstiness, and the conditions in host behavior that result in poor performance at the router. Previous research, however, has focused on router performance with heavy-tailed traffic as input, leaving some broader performance-related problems unaddressed. ^ This dissertation addresses three problems. First, a model of end-to-end delay in the presence of heavy-tailed traffic is presented, offering some insights for congestion control mechanisms. Second, we construct a model that represents network traffic as a confluence of independent streams with arbitrary ON-time distributions, and provide an analysis of its performance effects on the router. Lastly, we present some results revealing the interplay among payload-to-header size ratio, degree of traffic burstiness, and mean router delay. The performance models presented employ semi-Markov processes, and are formulated using a Linear Algebraic Queueing framework. With semi-Markov processes at the core of modeling, this dissertation provides a further testimonial of their broad expressive powers in representing complex behavior. ^