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HEAVY TRAFFIC LIMITS VIA BROWNIAN EMBEDDINGS

Published online by Cambridge University Press:  19 September 2006

Erol A. Peköz  and
Jose Blanchet
Erol A. Peköz
Affiliation:
Boston University School of Management, Boston, MA 02215, E-mail: pekoz@bu.edu
Jose Blanchet
Affiliation:
Harvard University, Statistics Department, Cambridge, MA 02138, E-mail: blanchet@stat.harvard.edu
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Abstract

For the GI/GI/1 queue we show that the scaled queue size converges to reflected Brownian motion in a critical queue and converges to reflected Brownian motion with drift for a sequence of subcritical queuing models that approach a critical model. Instead of invoking the topological argument of the usual continuous-mapping approach, we give a probabilistic argument using Skorokhod embeddings in Brownian motion.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 595 - 598
Copyright
© 2006 Cambridge University Press

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References

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