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9096 results in Communications, Signal Processing and Information Theory

Page 69 of 455

  • 6 - Scaling of G/G/1 and G/G/∞

  • from Part II - Approximations of the Single Queue
  • Gideon Weiss, University of Haifa, Israel
  • Book:
    Scheduling and Control of Queueing Networks
    Published online:
    01 October 2021
    Print publication:
    14 October 2021, pp 83-101

  • Summary

    We discuss fluid and diffusion approximations to the GI/GI/1 queue by scaling time and space. We also introduce the GI/GI/1 queueing system and study it under many-server scaling. The three types of scaling, fluid, diffusion, and many-server, form the backbone for Parts IV, V, andVI of the book, where we use them to study networks of queues. These approximations allow us to obtain a much better idea of how queues evolve over time than can be obtained from an exact discrete state Markov description.

Scheduling and Control of Queueing Networks
  • Gideon Weiss
  • Published online:
    01 October 2021
    Print publication:
    14 October 2021
  • Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin–Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

Page 69 of 455