Heavy Traffic Analysis of Controlled Queueing and Communication Networks

This book provides a thorough development of the powerful methods of heavy traffic analysis and approximations with applications to a wide variety of shastic (e.g. queueing and communication) networks, for both controlled and uncontrolled systems. The approximating models are reflected shastic differential equations. The analytical and numerical methods yield considerable simplifications and insights and good approximations to both path properties and optimal controls under broad conditions on the data and structure. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest. Control problems in telecommunications and applications to scheduling, admissions control, polling, and elsewhere are treated. The necessary probability background is reviewed, including a detailed survey of reflected shastic differential equations, weak convergence theory, methods for characterizing limit processes, and ergodic problems.