Research on Applied Probability Models

University Of Arizona, Tucson AZ

Investigators

Abstract

The research project is for the development of integrated methodology consisting of mathematical analysis, algorithms, and computer experimentation for systems involving probabilistic behavior. The long-term goal is to quantify properties of embedded point processes. In this project a variety of important queuing problems will be studied from this perspective with the intent of developing a physical understanding of these systems. This research will be performed in collaboration with a group of distinguished international colleagues to investigate questions such as the following: (1) What is the behavior of the system between significant runs of increments or decrements? (2) During transient phases, is the output stream more or less regular than the input stream? (3) Does the input-output stream have fundamentally different behavioral characteristics at different levels of traffic intensity? and (4) How does the distribution of time until a new maximum queue length evolve with the system state and time? Research results on the use of matrix-geometric methods to obtain the moments of these systems will be extended and utilized in this project. The proposed methodology has widespread applicability, particularly to telecommunication, biological, and manufacturing systems. The results of this research can lead to improved methods for designing stochastic systems. The intuition developed from the problems studied can lead to guidelines for system design that replace wasteful trial and error and costly simulation. The mathematical methods developed may allow accurate performance prediction of proposed system designs and can enable analysts to produce probabilistic estimates for the occurrence of various combined events. System managers may be able to more effectively allocate resources to operate these systems and to avoid congestion and losses. The results can lead to intelligent decisions for expanding system capacity and for early detection of changes in system performance ensuring satisfactory customer service without excessive investment.