Free Access
Volume 12, Number 4, October 2006
Page(s) 662 - 698
Published online 11 October 2006
  1. R. Atar and P. Dupuis, A differential game with constrained dynamics and viscosity solutions of a related HJB equation. Nonlinear Anal. 51 (2002) 1105–1130. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Atar, P. Dupuis and A. Shwartz, An escape criterion for queueing networks: Asymptotic risk-sensitive control via differential games. Math. Op. Res. 28 (2003) 801–835. [CrossRef] [Google Scholar]
  3. R. Atar, P. Dupuis and A. Schwartz, Explicit solutions for a network control problem in the large deviation regime, Queueing Systems 46 (2004) 159–176. [Google Scholar]
  4. F. Avram, Optimal control of fluid limits of queueing networks and stochasticity corrections, in Mathematics of Stochastic Manufacturing Systems, G. Yin and Q. Zhang Eds., AMS, Lect. Appl. Math. 33 (1996). [Google Scholar]
  5. F. Avram, D. Bertsimas, M. Ricard, Fluid models of sequencing problems in open queueing networks; and optimal control approach, in Stochastic Networks, F.P. Kelly and R.J. Williams Eds., Springer-Verlag, NY (1995). [Google Scholar]
  6. J.A. Ball, M.V. Day and P. Kachroo, Robust feedback control of a single server queueing system. Math. Control, Signals, Syst. 12 (1999) 307–345. [Google Scholar]
  7. J.A. Ball, M.V. Day, P. Kachroo and T. Yu, Robust L2-Gain for nonlinear systems with projection dynamics and input constraints: an example from traffic control. Automatica 35 (1999) 429–444. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Bardi and I. Cappuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Boston (1997). [Google Scholar]
  9. T. Basar and P. Bernhard, H-Optimal Control and Related Minimax Design Problems – A Dynamic game approach. Birkhäuser, Boston (1991). [Google Scholar]
  10. A. Budhiraja and P. Dupuis, Simple necessary and sufficient conditions for the stability of constrained processes. SIAM J. Appl. Math. 59 (1999) 1686–1700. [CrossRef] [MathSciNet] [Google Scholar]
  11. H. Chen and A. Mandelbaum, Discrete flow networks: bottleneck analysis and fluid approximations. Math. Oper. Res. 16 (1991) 408–446. [CrossRef] [MathSciNet] [Google Scholar]
  12. H. Chen and D.D. Yao, Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization. Springer-Verlag, N.Y. (2001). [Google Scholar]
  13. J.G. Dai, On the positive Harris recurrence for multiclass queueing networks: a unified approach via fluid models. Ann. Appl. Prob. 5 (1995) 49–77. [Google Scholar]
  14. M.V. Day, On the velocity projection for polyhedral Skorokhod problems. Appl. Math. E-Notes 5 (2005) 52–59. [MathSciNet] [Google Scholar]
  15. M.V. Day, J. Hall, J. Menendez, D. Potter and I. Rothstein, Robust optimal service analysis of single-server re-entrant queues. Comput. Optim. Appl. 22 (2002), 261–302. [Google Scholar]
  16. P. Dupuis and H. Ishii, On Lipschitz continuity of the solution mapping of the Skorokhod problem, with applications. Stochastics and Stochastics Reports 35 (1991) 31–62. [MathSciNet] [Google Scholar]
  17. P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities. Annals Op. Res. 44 (1993) 9–42. [Google Scholar]
  18. P. Dupuis and K. Ramanan, Convex duality and the Skorokhod problem, I and II. Prob. Theor. Rel. Fields 115 (1999) 153–195, 197–236. [CrossRef] [Google Scholar]
  19. D. Eng, J. Humphrey and S. Meyn, Fluid network models: linear programs for control and performance bounds in Proc. of the 13th World Congress of International Federation of Automatic Control B (1996) 19–24. [Google Scholar]
  20. A.F. Filippov, Differential Equations with Discontinuous Right Hand Sides, Kluwer Academic Publishers (1988). [Google Scholar]
  21. W.H. Fleming and M.R. James, The risk-sensitive index and the H2 and H morms for nonlinear systems. Math. Control Signals Syst. 8 (1995) 199–221. [CrossRef] [Google Scholar]
  22. W.H. Fleming and W.M. McEneaney, Risk-sensitive control on an infinite time horizon. SAIM J. Control Opt. 33 (1995) 1881–1915. [CrossRef] [Google Scholar]
  23. J.M. Harrison, Brownian models of queueing networks with heterogeneous customer populations, in Proc. of IMA Workshop on Stochastic Differential Systems. Springer-Verlag (1988). [Google Scholar]
  24. P. Hartman, Ordinary Differential Equations (second edition). Birkhauser, Boston (1982). [Google Scholar]
  25. R. Isaacs, Differential Games. Wiley, New York (1965). [Google Scholar]
  26. P.L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (1985) 793–820. [Google Scholar]
  27. X. Luo and D. Bertsimas, A new algorithm for state-constrained separated continuous linear programs. SIAM J. Control Opt. 37 (1998) 177–210. [CrossRef] [Google Scholar]
  28. S. Meyn, Stability and optimizations of queueing networks and their fluid models, in Mathematics of Stochastic Manufacturing Systems, G. Yin and Q. Zhang Eds., Lect. Appl. Math. 33, AMS (1996). [Google Scholar]
  29. S. Meyn, Transience of multiclass queueing networks via fluid limit models. Ann. Appl. Prob. 5 (1995) 946–957. [CrossRef] [Google Scholar]
  30. S. Meyn, Sequencing and routing in multiclass queueing networks, part 1: feedback regulation. SIAM J. Control Optim. 40 (2001) 741–776. [CrossRef] [MathSciNet] [Google Scholar]
  31. M.I. Reiman, Open queueing networks in heavy traffic. Math. Oper. Res. 9 (1984) 441–458. [Google Scholar]
  32. R.T. Rockafellar, Convex Analysis. Princeton Univ. Press, Princeton (1970). [Google Scholar]
  33. P. Soravia, H control of nonlinear systems: differential games and viscosity solutions. SIAM J. Control Optim. 34 (1996) 071–1097. [Google Scholar]
  34. G. Weiss, On optimal draining of re-entrant fluid lines, in Stochastic Networks, F.P. Kelly and R.J. Williams, Eds. Springer-Verlag, NY (1995). [Google Scholar]
  35. G. Weiss, A simplex based algorithm to solve separated continuous linear programs, to appear (preprint available at [Google Scholar]
  36. P. Whittle, Risk-sensitive Optimal Control. J. Wiley, Chichester (1990). [Google Scholar]
  37. R.J. Williams, Semimartingale reflecting Brownian motions in the orthant, Stochastic Networks, Springer, New York IMA Vol. Math. Appl. 71 (1995) 125–137. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.