This IMA Volume in Mathematics and its Applications STOCHASTIC NETWORKS is based on the proceedings of a workshop that was an integral part of the 1993-94 IMA program on Emerging Applications of Probability. We thank Frank P. Kelly and Ruth J. Williams for organizing the workshop and for editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Air Force Office of Scientific Research, the Army Research Office, and the National Security Agency, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE Research on stochastic networks has powerful driving applications in the modelling of manufacturing, telecommunications, and computer sys tems. These various applications have raised common mathematical issues of some subtlety, and a notable feature of the workshop was the way in which experts in different areas such as operations research, systems science and engineering, and applied mathematics have been attacking important problems from different viewpoints.