Data-analytic and monitoring schemes for a class of discrete point processes.

Abstract

A point process model for the packet stream arising in teletraffic processes is the discrete, non-negative integer-valued, stationary process introduced by Neuts and Pearce. In this thesis, we examine an empirical approach to develop a monitoring scheme for that point process. Monitoring is a procedure of tracking a stochastic process to identify quickly the development of anomalous situations in the evolution of that process and detect their assignable causes. Further, a data-analytic scheme to evaluate the order of a Markov chain that quantifies the local dependence embedded in the point process and Walsh spectral techniques are examined.