Wardrop Equilibria with Risk-Averse Users

References

• Aashtiani H. Z., Magnanti T. L. Equilibria on a congested transportation network. SIAM J. Algebraic Discrete Methods (1981) 2(3):213–226Crossref, Google Scholar
• Aghassi M., Bertsimas D. Robust game theory. Math. Programming (2006) 107B:231–273Crossref, Google Scholar
• Altman E., Boulogne T., El-Azouzi R., Jiménez T., Wynter L. A survey on networking games in telecommunications. Comp. Oper. Res. (2006) 33(2):286–311Crossref, Google Scholar
• Andreatta G., Romeo L. Stochastic shortest paths with recourse. Networks (1988) 18:193–204Crossref, Google Scholar
• Ashlagi I., Monderer D., Tennenholtz M. Resource selection games with unknown number of players. Proc. Fifth Internat. Joint Conf. Autonomous Agents Multiagent Systems (2006) (ACM, New York) 819–825Crossref, Google Scholar
• Atamtürk A., Zhang M. Two-stage robust network flow and design under demand uncertainty. Oper. Res. (2007) 55(4):662–673Link, Google Scholar
• Bar-Gera H. Transportation network test problems. (2002) . Accessed November 2009, http://www.bgu.ac.il/∼bargera/tntp/Google Scholar
• Beckmann M. J., McGuire C. B., Winsten C. B.Studies in the Economics of Transportation (1956) (Yale University Press, New Haven, CT) Google Scholar
• Bell M. G. H., Cassir C. Risk-averse user equilibrium traffic assignment: An application of game theory. Transportation Res. (2002) 36B(8):671–681Crossref, Google Scholar
• Ben-Tal A., Nemirovski A. Robust truss topology design via semidefinite programming. SIAM J. Optim. (1997) 7(4):991–1016Crossref, Google Scholar
• Ben-Tal A., Nemirovski A. Robust convex optimization. Math. Oper. Res. (1998) 23(4):769–805Link, Google Scholar
• Ben-Tal A., Golany B., Nemirovski A., Vial J.-P. Supplier-retailer flexible commitments contracts: A robust optimization approach. Manufacturing Service Oper. Management (2005) 7(3):248–273Link, Google Scholar
• Bergendorff P., Hearn D. W., Ramana M. V., Pardalos P. M., Hearn D. W., Hager W. W. Congestion toll pricing of traffic networks. Network Optimization, Lecture Notes in Economics and Mathematical Systems (1997) 450(Springer, Berlin) 51–71Crossref, Google Scholar
• Bertsekas D. P., Tsitsiklis J. N. An analysis of stochastic shortest path problems. Math. Oper. Res. (1991) 16(3):580–595Link, Google Scholar
• Bertsimas D., Sim M. Robust discrete optimization and network flows. Math. Programming Ser. B (2003) 98:49–71Crossref, Google Scholar
• Bertsimas D., Thiele A., Bienstock D., Nemhauser G. A robust optimization approach to supply chain management. Proc. 10th Internat. Integer Programming Combin. Optim. Conf. (2004) 3064(Springer, Berlin/Heidelberg) 86–100IT Lecture Notes in Computer ScienceCrossref, Google Scholar
• Bertsimas D., Thiele A. A robust optimization approach to inventory theory. Oper. Res. (2006) 54(1):150–168Link, Google Scholar
• Braess D. Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung (1968) 12:258–268[English translation: Braess, D., A. Nagurney, T. Wakolginger. 2005. On a paradox of traffic planning. Transportation Sci. 39(4) 446–450]Google Scholar
• Bureau of Public Roads Traffic assignment manual. (1964) . U.S. Department of Commerce, Urban Planning Division, Washington, DCGoogle Scholar
• Dafermos S. C. Traffic equilibrium and variational inequalities. Transportation Sci. (1980) 14(1):42–54Link, Google Scholar
• Daganzo C., Sheffi Y. On stochastic models of traffic assignment. Transportation Sci. (1977) 11(3):253–274Link, Google Scholar
• de Palma A., Nesterov Y. Optimization formulations and static equilibrium in congested transportation networks. (1998) . CORE Discussion Paper 9861, Université Catholique de Louvain, Louvain-la-Neuve, BelgiumGoogle Scholar
• de Palma A., Picard N. Route choice decision under travel time uncertainty. Transportation Res. (2005) 39A(4):295–324Google Scholar
• Dial R. B. A probabilistic multi-path traffic assignment algorithm which obviates path enumeration. Transportation Res. (1971) 5(2):83–111Crossref, Google Scholar
• El-Ghaoui L., Lebret H. Robust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. (1997) 18:1035–1064Crossref, Google Scholar
• El-Ghaoui L., Oks M., Oustry F. Worst-case value-at-risk and robust portfolio optimization: A conic programming approach. Oper. Res. (2003) 51(4):543–556Link, Google Scholar
• El-Ghaoui L., Oustry F., Lebret H. Robust solutions to uncertain semidefinite programs. SIAM J. Optim. (1998) 9(1):33–52Crossref, Google Scholar
• Fan Y. Y., Kalaba R. E., Moore J. E. Arriving on time. J. Optim. Theory Appl. (2005a) 127(3):497–513Crossref, Google Scholar
• Fan Y. Y., Kalaba R. E., Moore J. E. Shortest paths in stochastic networks with correlated link costs. Comput. Math. Appl. (2005b) 49:1549–1564Crossref, Google Scholar
• Ferris M. C., Mangasarian O. L., Pang J. S.Complementarity: Applications, Algorithms and Extensions, Vol. 50, Applied Optimization (2001) (Kluwer Academic, Dordrecht, The Netherlands) Crossref, Google Scholar
• Fleischer L., Jain K., Mahdian M. Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. Proc. 45th Annual IEEE Sympos. Foundations Comput. Sci. (2004) (IEEE Computer Society Press, Los Alamitos, CA) 277–285Crossref, Google Scholar
• Fourer R., Gay D. M., Kernighan B. W.AMPL: A Modeling Language for Mathematical Programming (2002) (Brooks/Cole, Pacific Groove, CA) Google Scholar
• Gabriel S., Bernstein D. The traffic equilibrium problem with nonadditive path costs. Transportation Sci. (1997) 31:337–348Link, Google Scholar
• Goldfarb D., Iyengar G. Robust portfolio selection problems. Math. Oper. Res. (2003) 28(1):1–38Link, Google Scholar
• Harsanyi J. C. Games with incomplete information played by “Bayesian” players, I–III. Part I. The basic model. Management Sci. (1967) 14(3):159–182Link, Google Scholar
• Harsanyi J. C. Games with incomplete information played by “Bayesian” players, I–III. Part II. Bayesian equilibrium points. Management Sci. (1968) 14(5):320–334Link, Google Scholar
• Hayashi S., Yamashita N., Fukushima M. Robust Nash equilibria and second-order cone complementarity problems. J. Nonlinear Convex Anal. (2005) 6:283–296Google Scholar
• Holmström B., Myerson R. B. Efficient and durable decision rules with incomplete information. Econometrica (1983) 51:1799–1820Crossref, Google Scholar
• ILOG CPLEX. (2005) . http://www.ilog.comGoogle Scholar
• Jahn O., Möhring R. H., Schulz A. S., Stier-Moses N. E. System-optimal routing of traffic flows with user constraints in networks with congestion. Oper. Res. (2005) 53(4):600–616Link, Google Scholar
• Liu H., Ban X., Ran B., Mirchandani P. An analytical dynamic traffic assignment model with stochastic network and travelers' perceptions. Transportation Res. Record (2002) 1783:125–133Crossref, Google Scholar
• Lo H. K., Tung Y.-K. Network with degradable links: Capacity analysis and design. Transportation Res. (2003) 37B(4):345–363Crossref, Google Scholar
• Marcotte P., Zhu D. L. Existence and computation of optimal tolls in multiclass network equilibrium problems. Oper. Res. Lett. (2009) 37:211–214Crossref, Google Scholar
• Mirchandani P. B., Soroush H. Generalized traffic equilibrium with probabilistic travel times and perceptions. Transportation Sci. (1987) 21:133–152Link, Google Scholar
• Nagurney A.Network Economics: A Variational Inequality Approach (1999) 2nd ed.(Kluwer Academic, Dordrecht, The Netherlands) Crossref, Google Scholar
• Nie Y., Wu X. Shortest path problem considering on-time arrival probability. Transportation Res. (2009) 43B:597–613Crossref, Google Scholar
• Nikolova E., Brand M., Karger D. R. Optimal route planning under uncertainty. Proc. Internat. Conf. Automated Planning Scheduling (2006) Cumbria, UK:131–141Google Scholar
• Noland R. B., Small K., Koskenoja P., Chu X. Simulating travel reliability. Regional Sci. Urban Econom. (1998) 28(5):535–564Crossref, Google Scholar
• Ordóñez F., Stier-Moses N. E. Robust wardrop equilibrium. Proc. First Inter. Conf. Network Control Optim. (2007a) 4465(Springer, Berlin) 247–256Lecture Notes in Comput. Sci.Crossref, Google Scholar
• Ordóñez F., Zhao J. Robust capacity expansion of network flows. Networks (2007b) 50(2):136–145Crossref, Google Scholar
• Patriksson M.The Traffic Assignment Problem: Models and Methods (1994) (VSP, Utrecht, The Netherlands) Google Scholar
• Roughgarden T. How unfair is optimal routing? Proc. 13th Annual ACM-SIAM Sympos. Discrete Algorithms (2002) (SIAM, Philadelphia) 203–204Google Scholar
• Roughgarden T., Tardos É. How bad is selfish routing? J. ACM (2002) 49:236–259Crossref, Google Scholar
• Sheffi Y.Urban Transportation Networks (1985) (Prentice-Hall, Englewood, NJ) Google Scholar
• Smith M. J. The existence, uniqueness and stability of traffic equilibria. Transportation Res. (1979) 13B:295–304Crossref, Google Scholar
• Uchida T., Iida Y., Daganzo C. F. Risk assignment: A new traffic assignment model considering risk of travel time variation. Proc. 12th Internat. Sympos. Transportation Traffic Theory (1993) (Elsevier, Amsterdam) 89–105Google Scholar
• Ukkusuri S. V., Waller S. T. Approximate expressions for network performance under demand uncertainty. Transportation Lett. (2010) . ForthcomingCrossref, Google Scholar
• Vanderbei R. J. LOQO: An interior point code for quadratic programming. Optim. Methods Software (1999) 12:451–484Crossref, Google Scholar
• Wardrop J. G. Some theoretical aspects of road traffic research. Proc. Institute of Civil Engineers, Part II (1952) 1:325–378Crossref, Google Scholar
• Yang H., Huang H.-J. The multi-class, multi-criteria traffic network equilibrium and systems optimum problem. Transportation Res. (2004) 38B:1–15Crossref, Google Scholar