Free Access
Issue
ESAIM: COCV
Volume 12, Number 4, October 2006
Page(s) 662 - 698
DOI https://doi.org/10.1051/cocv:2006016
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 http://stat.haifa.ac.il/~gweiss/). [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]

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