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Brownian Approximations

  • Chapter
Fundamentals of Queueing Networks

Part of the book series: Stochastic Modelling and Applied Probability ((SMAP,volume 46))

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Abstract

The purpose of this chapter is to develop a general approach to approximating a multiclass queueing network by a semimartingale reflected Brownian motion, (SRBM), which is a generalization of the RBM studied earlier. Our focus is not on proving limit theorems so as to justify why the network in question can be approximated by an SRBM (as we did in several previous chapters). Rather our intention is to illustrate how to approximate the network by an SRBM. We make no claim that the proposed approximation can always be justified by some limit theorems. To the contrary, through both analysis and numerical results, we identify cases where the SRBM may not exist, or may work poorly. (A complete characterization of when the proposed approximation works is a challenging and active research topic; refer to Section 10.7 for a survey on the recent advances in this research area.)

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Authors and Affiliations

  1. Faculty of Commerce and Business Administration, University of British Columbia, V6T 1Z2, Vancouver, British Columbia, Canada

    Hong Chen

  2. Department of Operations Research and Industrial Engineering, Columbia University, 10027, New York, NY, USA

    David D. Yao

Authors
  1. Hong Chen
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  2. David D. Yao
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© 2001 Springer Science+Business Media New York

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Chen, H., Yao, D.D. (2001). Brownian Approximations. In: Fundamentals of Queueing Networks. Stochastic Modelling and Applied Probability, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5301-1_10

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  • DOI: https://doi.org/10.1007/978-1-4757-5301-1_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2896-2

  • Online ISBN: 978-1-4757-5301-1

  • eBook Packages: Springer Book Archive

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