Hostname: page-component-7dd5485656-2pp2p Total loading time: 0 Render date: 2025-10-29T09:14:53.296Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Billingsley P. (1968). Convergence of probability measures. New York: Wiley.
Chen, H. & Yao, D.D. (2001). Fundamentals of queueing networks. Performance, asymptotics, and optimization. New York: Springer-Verlag.
Durrett, R. (2005). Probability: Theory and examples, 3rd ed. Belmont, CA: Duxbury Press.
Kingman, J.F.C. (1965) The heavy traffic approximation in the theory of queues. Proceedings Symposium on Congestion Theory (Chapel Hill, N.C., 1964), pp. 137–169. Chapel Hill: University of North Carolina Press.
Obłój, J. (2004). The Skorokhod embedding problem and its offspring. Probability Surveys 1: 321–390.Google Scholar
Robert, P. (2003). Stochastic networks and queues. Berlin: Springer-Verlag.
Rosenkrantz, W.A. (1980). On the accuracy of Kingman's heavy traffic approximation in the theory of queues. Zeitschrift für Wahrscheinlichkeitstheorie und Verwund Gebiete 51(1): 115–121.Google Scholar
Skorokhod, A.V. (1965). Studies in the theory of random processes. Reading, MA: Addison-Wesley Publishing.
Whitt, W. (2002). Stochastic-process limits. An introduction to stochastic-process limits and their application to queues. New York: Springer-Verlag.