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]
  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]
  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.
  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).
  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).
  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.
  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]
  8. M. Bardi and I. Cappuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Boston (1997).
  9. T. Basar and P. Bernhard, H-Optimal Control and Related Minimax Design Problems – A Dynamic game approach. Birkhäuser, Boston (1991).
  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]
  11. H. Chen and A. Mandelbaum, Discrete flow networks: bottleneck analysis and fluid approximations. Math. Oper. Res. 16 (1991) 408–446. [CrossRef] [MathSciNet]
  12. H. Chen and D.D. Yao, Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization. Springer-Verlag, N.Y. (2001).
  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.
  14. M.V. Day, On the velocity projection for polyhedral Skorokhod problems. Appl. Math. E-Notes 5 (2005) 52–59. [MathSciNet]
  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.
  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]
  17. P. Dupuis and A. Nagurney, Dynamical systems and variational inequalities. Annals Op. Res. 44 (1993) 9–42.
  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]
  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.
  20. A.F. Filippov, Differential Equations with Discontinuous Right Hand Sides, Kluwer Academic Publishers (1988).
  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]
  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]
  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).
  24. P. Hartman, Ordinary Differential Equations (second edition). Birkhauser, Boston (1982).
  25. R. Isaacs, Differential Games. Wiley, New York (1965).
  26. P.L. Lions, Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (1985) 793–820.
  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]
  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).
  29. S. Meyn, Transience of multiclass queueing networks via fluid limit models. Ann. Appl. Prob. 5 (1995) 946–957. [CrossRef]
  30. S. Meyn, Sequencing and routing in multiclass queueing networks, part 1: feedback regulation. SIAM J. Control Optim. 40 (2001) 741–776. [CrossRef] [MathSciNet]
  31. M.I. Reiman, Open queueing networks in heavy traffic. Math. Oper. Res. 9 (1984) 441–458. [CrossRef] [MathSciNet]
  32. R.T. Rockafellar, Convex Analysis. Princeton Univ. Press, Princeton (1970).
  33. P. Soravia, H control of nonlinear systems: differential games and viscosity solutions. SIAM J. Control Optim. 34 (1996) 071–1097.
  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).
  35. G. Weiss, A simplex based algorithm to solve separated continuous linear programs, to appear (preprint available at
  36. P. Whittle, Risk-sensitive Optimal Control. J. Wiley, Chichester (1990).
  37. R.J. Williams, Semimartingale reflecting Brownian motions in the orthant, Stochastic Networks, Springer, New York IMA Vol. Math. Appl. 71 (1995) 125–137.