## Doctoral Dissertations

#### Title

Modeling telecommunication systems with self-similar data traffic

January 1998

#### Keywords

Engineering, Electronics and Electrical|Operations Research|Computer Science

Ph.D.

#### Abstract

In this dissertation we present a means to study queueing systems which exhibit self-similarity and long-range dependencies (LRD). The $PT\otimes\lambda$ process is created, and we illustrate this process is asymptotically self-similar and demonstrate that it exhibits LRD in its interarrival stream. Our results are significant since this is the first analytic queueing model developed and studied which exhibits self-similarity and LRD behavior in both its interarrival and counting processes. As a result, we are able to demonstrate analytically, via SM/M/1 queueing analysis, that removing LRD improves queueing performance. This is consistent with empirical studies performed on network traffic traces. We go on to analytically show that renewal processes represent performance bounds for the $(PT\otimes\lambda)/M/1$ queue. That is, the PT/M/1 queue is the upper bound for performance measurements while the M/M/1 queue is the lower bound. Finally, we explore the notion of how likely it is to observe power-tail renewal processes in real-world teletraffic scenarios. ^

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