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Heavy Traffic Limits for Multiphase Queues
F. I. Karpelevich and A. Ya. Kreinin

Translations of Mathematical Monographs
1994; 143 pp; hardcover
Volume: 137
ISBN-10: 0-8218-4597-7
ISBN-13: 978-0-8218-4597-4
List Price: US$74
Member Price: US$59.20
Order Code: MMONO/137
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This book analyzes several types of queueing systems arising in network theory and communication theory. Karpelevich and Kreinin use numerous methods and results from the theory of stochastic processes. The main emphasis is on problems of diffusion approximation of stochastic processes in queueing systems and on results based on applications of the hydrodynamic limit method. The book will be useful to researchers working in the theory and applications of queueing theory and stochastic processes.


Researchers working in the theory and applications of queueing theory and stochastic processes.


"The authors have done an excellent work to unify several approximation techniques. This is a high quality contribution to the scope, theory and methodology of multiphase queueing systems in terms of its lucid presentation, insights and directions. Researchers in this field will find this outstanding monograph. very useful."

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • Processes with reflection
  • Multiphase systems
  • Limit theorems for queue length and departure times processes
  • Appendix I. Weak convergence in function spaces
  • Appendix II. Weak convergence of functionals of stochastic processes
  • Appendix III. Auxiliary results
  • Appendix IV. Tandem queues in heavy traffic
  • Appendix V. Joint distributions in Poissonian tandem queues
  • Bibliographical notes
  • Bibliograpy
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