Asymptotics of the first hitting times of Markov jump processes with applications to ATM.

Abstract

This dissertation has three parts. The first part (Chapter 2) is about the asymptotics of the distribution of the first hitting time of a forbidden set by a Markov jump process. Explicit error bounds for the departure of the hitting time distribution from exponentiality are provided. The second part (Chapter 3 and Chapter 4, joint with Ian Iscoe and David McDonald) discusses the capacity of an ATM multiplexor in terms of the probability distribution of the time until the first occurrence of an excessive demand for bandwidth. In the third part (Chapter 5), the problem of the buffer overflow of an ATM multiplexor is studied. The methods developed give an excellent approximation for the steady-state probabilities of the contents of a buffer driven by heterogeneous sources.