Analysis and Simplifications of Discrete Event Systems and Jackson Queueing Networks.

摘要

This dissertation contians studies in two related areas: Discrete Event Systems Theory and Queueing Network Theory. In the first line of study, deterministic discrete event systems are modeled by formal automata- like structures, and a hierarchy of morphic relations among them is developed. A canonical representation of stochastic discrete event systems in coordinate probability space is proposed, and a hierarchy of morphic relations among them is constructed by means of measure preserving transformations. In the second line of study, several operating characteristics of the class of Jackson queueing networks are investiaged. Included are: line sizes (network state), total service awarded to customers, and traffic processes on the arcs. Special emphasis is placed on rigorous derivations of results from solid mathematical and statistical foundations. In the process, a number of theoretical gaps in the extant theory of state equilibrium are closed, and Burke's Theorem is extended from M/M/1 queues to Jackson networks with single server nodes.