Stochastic Networks

1. Front Matter

   Pages iii-xii

   PDF

2. Stability

   1. Global Stability of Two-Station Queueing Networks

      • J. G. Dai, John H. Vande Vate

      Pages 1-26

   2. Stable Priority Disciplines for Multiclass Networks

      • Hong Chen, David D. Yao

      Pages 27-39

   3. Closed Queueing Networks in Heavy Traffic: Fluid Limits and Efficiency

      • Sunil Kumar, P. R. Kumar

      Pages 41-64

   4. Asymptotics and Uniform Bounds for Multiclass Queueing Networks

      • P. R. Kumar

      Pages 65-73

   5. Stability of Discrete-Time Jackson Networks with Batch Movements

      • Masakiyo Miyazawa

      Pages 75-93

   6. Stability for Queues with Time Varying Rates

      • William A. Massey

      Pages 95-107

3. Rare Events

   1. Nonparametric Estimation of Tail Probabilities for the Single-Server Queue

      • Peter W. Glynn, Marcelo Torres

      Pages 109-138

   2. Rational Interpolation for Rare Event Probabilities

      • Wei-Bo Gong, Soracha Nananukul

      Pages 139-168

   3. Overloading Parallel Servers when Arrivals Join the Shortest Queue

      • David McDonald

      Pages 169-196

   4. Rare Events in the Presence of Heavy Tails

      • Søren Asmussen

      Pages 197-214

   5. A Network Multiplexer with Multiple Time Scale and Subexponential Arrivals

      • Predrag R. Jelenković, Aurel A. Lazar

      Pages 215-235

   6. Networks of Queues with Long-Range Dependent Traffic Streams

      • Venkat Anantharam

      Pages 237-256

   7. Fractional Brownian Approximations of Queueing Networks

      • Takis Konstantopoulos, Si-Jian Lin

      Pages 257-273

   8. Moderate Deviations for Queues with Long-Range Dependent Input

      • Cheng-Shang Chang, David D. Yao, Tim Zajic

      Pages 275-298

4. Back Matter

   Pages 299-300

   PDF

Two of the most exciting topics of current research in stochastic networks are the complementary subjects of stability and rare events - roughly, the former deals with the typical behavior of networks, and the latter with significant atypical behavior. Both are classical topics, of interest since the early days of queueing theory, that have experienced renewed interest mo­ tivated by new applications to emerging technologies. For example, new stability issues arise in the scheduling of multiple job classes in semiconduc­ tor manufacturing, the so-called "re-entrant lines;" and a prominent need for studying rare events is associated with the design of telecommunication systems using the new ATM (asynchronous transfer mode) technology so as to guarantee quality of service. The objective of this volume is hence to present a sample - by no means comprehensive - of recent research problems, methodologies, and results in these two exciting and burgeoning areas. The volume is organized in two parts, with the first part focusing on stability, and the second part on rare events. But it is impossible to draw sharp boundaries in a healthy field, and inevitably some articles touch on both issues and several develop links with other areas as well. Part I is concerned with the issue of stability in queueing networks.

• Jackson network
• Rang
• probability
• stochastic network
• combinatorics

• Department of Management Science and Operations Management, Columbia University, New York City, USA

  Paul Glasserman

• Department of Operations Research and Industrial Engineering, Columbia University, New York City, USA

  Karl Sigman, David D. Yao

Policies and ethics