Mathematical modelling and analysis of communication networks: transient characteristics of traffic processes and models for end-to-end delay and delay-jitter

The first part of the thesis (Part I) is devoted to find methods to describe transient behaviour of traffic processes, where the main emphasis is put on the description and analysis of excess periods and excess volumes of quite general stochastic processes. By assuming that traffic changes on different time scales, the transient characteristics such as excess periods could be important measures to describe periods of congestion on a communication link and moreover, the corresponding excess volume will represent lost information during such periods. Although the results obtained are of rather general nature, they provide some rather fundamental insight into transient characteristics of traffic processes. The distributions of the length of excess periods may then be expressed it terms of some excess probabilities that are related to the minimum of the process in the time interval considered. Similar relationsfor the excess volumes are harder to obtain and require the joint probability of the arrived volume and the minimum of the process in the same time interval