An Escape-Time Criterion for Queueing Networks: Asymptotic Risk-Sensitive Control via Differential Games
Published Online:1 Nov 2003https://doi.org/10.1287/moor.28.4.801.20514
References
- A differential game with constrained dynamics and viscosity solutions of a related HJB equation. Nonlinear Analysis (2002) 51(7):1105–1130Crossref, Google Scholar
- Explicit solutions to a network control problem in the large deviation regime. Queueing SystemsForthcomingGoogle Scholar
- Robust feedback control for a single server queueing system. Math. Control, Signals, Systems (1999a) 12:307–345Crossref, Google Scholar
- Robust L2-gain control for nonlinear systems with projection dynamics and input constraints: An example from traffic control. Automatica (1999b) 35:429–444Crossref, Google Scholar
- Two competing queues with geometric service requirements and linear costs: The μ-c rule is often optimal. Adv. Appl. Prob. (1985) 17:186–209Crossref, Google Scholar
- Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations (1997) (Birkhauser, Boston, MA) Crossref, Google Scholar
- Simple necessary and sufficient conditions for the stability of constrained processes. SIAM J. Appl. Math. (1999) 59:1686–1700Crossref, Google Scholar
- Hamilton-Jacobi equations with state constraints. Trans. AMS (1990) 318:643–683Crossref, Google Scholar
- Probabilités et Potentiel/Théorie des Martingales (1980) (Hermann, Paris, France) Google Scholar
- A Weak Convergence Approach to the Theory of Large Deviations (1997) (John Wiley & Sons, New York) Crossref, Google Scholar
- On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stochastics (1991a) 35:31–62Google Scholar
- On oblique derivative problems for fully nonlinear second-order elliptic PDE's on domains with corners. Hokkaido Math. J. (1991b) 20:135–164Crossref, Google Scholar
- Minimizing escape probabilities: A large deviations approach. SIAM J. Control Optim. (1989) 27(2):432–445Crossref, Google Scholar
- Risk-sensitive and robust escape criteria. SIAM J. Control Optim. (1997) 35(6):2021–2049Crossref, Google Scholar
- Dynamical systems and variational inequalities. Ann. Oper. Res. (1993) 44(1–4):9–42Google Scholar
- Convex duality and the Skorokhod problem. I, II. Probab. Theory Related Fields (1999) 2:153–195Crossref, Google Scholar
- Robust properties of risk-sensitive control. Math. Control, Signals Systems (2000) 13:318–332Crossref, Google Scholar
- The Existence of Value in Differential Games. Memoirs of the American Mathematical Society (1972) 126(American Mathematical Society, Providence, RI) Crossref, Google Scholar
- PDE-viscosity solution approach to some problems of large deviations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (1986) 13(2):171–192(4)Google Scholar
- Reflected Brownian motion on an orthant. Ann. Probab. (1981) 9(2):302–308Crossref, Google Scholar
- Time sharing service systems I. Theory Prob. Appl. (1974) 19:532–551Crossref, Google Scholar
- A boundary property of semimartingale reflecting Brownian motions. Probab. Theory Related Fields (1988) 77(1):87–97Crossref, Google Scholar
- Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
- Large Deviations for Performance Analysis (1995) (Chapman and Hall, London, U.K.) Google Scholar
- Optimal control with state space constraints I. SIAM J. Control Opt. (1986) 24:552–561Crossref, Google Scholar
- A note on ‘optimal control of a queueing system with two heterogeneous servers’. System Control Lett. (1984) 4:131–134Crossref, Google Scholar

