Brownian Approximations

  • Hong Chen
  • David D. Yao
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 46)


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.)


Stationary Distribution Service Capacity Service Discipline Reflection Mapping External Arrival 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Hong Chen
    • 1
  • David D. Yao
    • 2
  1. 1.Faculty of Commerce and Business AdministrationUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Operations Research and Industrial EngineeringColumbia UniversityNew YorkUSA

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