Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics and Stochastic Analysis
Volume 2007 (2007), Article ID 68958, 19 pages
http://dx.doi.org/10.1155/2007/68958
Research Article

Fluid Limits of Optimally Controlled Queueing Networks

1Department of Industrial Engineering and Operations Research, \newline Columbia University, New York 10027-6902, NY, USA
2Department of Mathematics, Virginia Tech, Blacksburg 24061-0123, VA, USA

Received 15 January 2007; Accepted 27 June 2007

Copyright © 2007 Guodong Pang and Martin V. Day. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. J. Kushner, Heavy Traffic Analysis of Controlled Queueing and Communication Networks, vol. 47 of Applications of Mathematics, Springer, New York, NY, USA, 2001. View at Zentralblatt MATH · View at MathSciNet
  2. R. Atar, P. Dupuis, and A. Shwartz, “An escape-time criterion for queueing networks: asymptotic risk-sensitive control via differential games,” Mathematics of Operations Research, vol. 28, no. 4, pp. 801–835, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. H. Chen and D. D. Yao, Fundamentals of Queueing Networks, vol. 46 of Applications of Mathematics, Springer, New York, NY, USA, 2001. View at Zentralblatt MATH · View at MathSciNet
  4. F. Avram, D. Bertsimas, and M. Ricard, “Fluid models of sequencing problems in open queueing networks; an optimal control approach,” in Stochastic Networks, F. P. Kelly and R. J. Williams, Eds., vol. 71 of IMA Vol. Math. Appl., pp. 199–234, Springer, New York, NY, USA, 1995. View at Zentralblatt MATH · View at MathSciNet
  5. S. P. Meyn, “Sequencing and routing in multiclass queueing networks—part I: feedback regulation,” SIAM Journal on Control and Optimization, vol. 40, no. 3, pp. 741–776, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. S. P. Meyn, “Sequencing and routing in multiclass queueing networks—part II: workload relaxations,” SIAM Journal on Control and Optimization, vol. 42, no. 1, pp. 178–217, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. N. Bäuerle, “Asymptotic optimality of tracking policies in stochastic networks,” The Annals of Applied Probability, vol. 10, no. 4, pp. 1065–1083, 2000. View at Zentralblatt MATH · View at MathSciNet
  8. J. Jacod, “Multivariate point processes: predictable projection, Radon-Nikodým derivatives, representation of martingales,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 31, pp. 235–253, 1975. View at Zentralblatt MATH · View at MathSciNet
  9. H. Chen and A. Mandelbaum, “Discrete flow networks: bottleneck analysis and fluid approximations,” Mathematics of Operations Research, vol. 16, no. 2, pp. 408–446, 1991. View at Zentralblatt MATH · View at MathSciNet
  10. A. Mandelbaum and G. Pats, “State-dependent stochastic networks—part I: approximations and applications with continuous diffusion limits,” The Annals of Applied Probability, vol. 8, no. 2, pp. 569–646, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. P. Brémaud, Point Processes and Queues: Martingale Dynamics, Springer Series in Statistics, Springer, New York, NY, USA, 1981. View at Zentralblatt MATH · View at MathSciNet
  12. L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Volume 2: Itô Calculus, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, New York, NY, USA, 1987. View at Zentralblatt MATH · View at MathSciNet
  13. L. C. G. Rogers and D. Williams, Diffusions, Markov Processes, and Martingales. Volume 1: Foundations, Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK, 2nd edition, 2000. View at Zentralblatt MATH · View at MathSciNet
  14. J. M. Harrison and M. I. Reiman, “Reflected Brownian motion on an orthant,” The Annals of Probability, vol. 9, no. 2, pp. 302–308, 1981. View at Zentralblatt MATH · View at MathSciNet
  15. P. Dupuis and H. Ishii, “On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications,” Stochastics and Stochastics Reports, vol. 35, no. 1, pp. 31–62, 1991. View at Zentralblatt MATH · View at MathSciNet
  16. M. V. Day, “Boundary-influenced robust controls: two network examples,” ESAIM: Control, Optimisation and Calculus of Variations, vol. 12, no. 4, pp. 662–698, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, New York, NY, USA, 1986. View at Zentralblatt MATH · View at MathSciNet
  18. H. J. Kushner and P. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, vol. 24 of Applications of Mathematics, Springer, New York, NY, USA, 2nd edition, 2001. View at Zentralblatt MATH · View at MathSciNet
  19. P. Billingsley, “Convergence of Probability Measures,” John Wiley & Sons, New York, NY, USA, 1968. View at Zentralblatt MATH · View at MathSciNet
  20. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, vol. 288 of Fundamental Principles of Mathematical Sciences, Springer, Berlin, Germany, 2nd edition, 2003. View at Zentralblatt MATH · View at MathSciNet