Some tools in modeling complex stochastic systems

Sweeping applications of digital computers have dramatically changed the plant that a control engineer faces. Today´s dynamic systems are often based on man-made protocols, driven by discrete events occurring at random times, and are huge in size or dimension. Examples, among many, are communication networks and computing systems. The difficulties for controlling these systems are the lack of analytical models, anarchism in using them (namely every user adds more applications to the system without a global view), and curse of dimensionality. The first step in the control and management of such systems is to develop efficient models so that the system behavior could be quickly evaluated. We have been trying to develop some tools for the modeling of various complex stochastic systems. In this paper we review the key concepts in some of these developments