Stochastic Networks

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.

Klappentext

In the past decade the proliferation of local and global communication networks for computer and human communication, the development of parallel computers with large numbers of processors, and the design of flexible and robust manufacturing systems have spurred major advances in our understanding of queuing volume reviews recent progress. While research on queuing networks uses many of the traditional queuing theory insights, it is more concerned with how network components interact than with detailed models of how an individual queue behaves. In the last few years there have been some surprises, in particular with regard to the conditions for stability of multiclass queuing networks, which is covered in this book. It also covers the challenges reflected Brownian motion has set both as a mathematical object and as a modelling paradigm; the usefulness of ideas from the interacting particle system world; the application of large deviation theory; and the developing connections with optimization and dynamical systems theory.

Inhalt
Balanced fluid models of multiclass queueing networks: a heavy traffic conjecture.- Scheduling queueing networks: stability, performance analysis and design.- Stability of open multiclass queueing networks via fluid models.- On optimal draining of re-entrant fluid lines.- Two badly behaved queueing networks.- Some badly behaved closed queueing networks.- Semimartingale reflecting Brownian motions in the orthant.- A control problem for a new type of public transportation system, via heavy traffic analysis.- Dynamic routing in stochastic networks.- On trunk reservation in loss networks.- Fluid models of sequencing problems in open queueing networks; an optimal control approach.- Convergence of departures from an infinite sequence of queues.- State-dependent queues: approximations and applications.- A state-dependent polling model with Markovian routing.- Starlike networks with synchronization constraints.- Matrix product-form solutions for Markov chains and a LCFS queue.- Large deviation analysis of queueing systems.- Stationary tail probabilities in exponential server tandems with renewal arrivals.- Large deviations for the infinite server queue in heavy traffic.- Traffic modeling for high-speed networks: theory versus practice.- Admission control for ATM networks.