Advanced discrete-time modeling and analysis in high-speed networks

The growth of telecommunication systems is more than ever stimulating the need for mathematical modeling and evaluation techniques to predict the performance of these systems. These techniques have become an indispensable tool for assessment of the performance of a system, evaluation of design alternatives, resource dimensioning, and system configuration.; A large class of tele-traffic models which arises naturally in high-speed telecommunication and computer networks can be analyzed through the matrix generalization of embedded discrete-time Markov chains. These chains can model a large class of systems involving packetized voice, data and video traffic.; This dissertation addresses several issues in discrete-time teletraffic modeling and analysis using the system theoretic approach for the purpose of evaluating the performance of high-speed networks.; First, we study a general discrete-time structured Markov chain so called "Combined M/G/1-G/M/1 Chain." We present a truncation free algorithm to obtain a matrix geometric solution of the chain. The presented solution technique analyzes efficiently the generator matrices by exploiting the rational structure of the generator matrix of a structured Markov chain.; Then, we analyze generic discrete-time queueing models with general distribution for correlated batch arrivals and departures. Our models allow distributions with arbitrary rational probability generating matrices. We use a state-space representation of the model resulting in an exact simple matrix geometric solution of the system probability vector. Our approach is algorithmic, numerically robust and efficient.; Finally, we study the performance analysis of an ATM multiplexer supporting both delay sensitive (e.g., voice) and loss sensitive (e.g., data) traffic flows. The delay sensitive cells are stored in a finite buffer and are given service priority over loss sensitive cells in each slot. We allow both classes to have a general (Markovian) correlation structure. A simple matrix geometric solution for the state probability of the system is provided allowing simple computation of any desired performance metric such as loss probability and buffer requirements of high and low priority classes, respectively. Also, we discuss how to obtain the Markov chain representation of discrete AutoRegressive models which are being used for modeling of traffic streams with short range dependency and high correlation such as video conferencing.