The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox

Anna Nagurney1,2, David C. Parkes3, Patrizia Daniele3,4
1Radcliffe Institute for Advanced Study, Harvard University, Cambridge, USA
2Department of Finance and Operations Management, Isenberg School of Management, University of Massachusetts, Amherst, USA
3Division of Engineering and Applied Sciences, Harvard University, Cambridge, USA
4Department of Mathematics and Computer Science, University of Catania, Catania, Italy

Tóm tắt

Từ khóa


Tài liệu tham khảo

Altman E, Boulogne T, El Azouzi R, Jimenez T, Wynter L (2005) A survey on networking games in telecommunications. INRIA, Cedex, France

Arnott R, De Palma A, Lindsey R. (1993) Properties of dynamic traffic equilibrium involving bottlenecks, including a paradox and metering. Transport Sci 27:148–160

Barbagallo A (2005) Regularity results for time-dependent variational inequalities and quasi-variational inequalities and computational procedures. Math Models Methods Appl Sci (in press)

Barbagallo A (2006) Regularity results for time-dependent degenerate variational inequalities and applications to time-dependent equilibrium problems. Comput Methods Appl Math 6 (in press)

Beckmann MJ (1967) On the theory of traffic flows in networks. Traffic Quart 21:109–116

Beckmann MJ, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Yale University Press, New Haven, CT

Bertsekas DP, Gallager RG (1987) Data networks. Prentice-Hall, Englewood Cliffs, NJ

Bertsekas DP, Tsitsiklis JN (1997) Parallel and distributed computation: Numerical methods. Prentice-Hall, Englewood Cliffs, NJ

Boyce DE, Mahmassani HS, Nagurney A (2005) A retrospective of Beckmann, McGuire, and Winsten’s Studies in the Economics of Transportation. Papers Reional Sci 84:85–103

Braess D (1968) Uber ein paradoxon aus der verkehrsplaning. Unternehmenforschung 12:258–268

Braess D, Nagurney A, Wakolbinger T (2005) On a paradox of traffic planning, translation of the 1968 article by Braess. Transport Sci 39:446–450

Brezis H (1967) Inequations D’Evolution Abstraites. C R Acad Sci

Cantor DG, Gerla M (1974) Optimal routing in a packet-switched computer network. IEEE Trans Comput 23:1062–1069

Cojocaru M-G, Daniele P, Nagurney A (2005a) Projected dynamical systems and evolutionary variational inequalities. J Optimizat Theory Appl 27:1–15

Cojocaru M-G, Daniele P, Nagurney A (2005b) Double-layered dynamics: a unified theory of projected dynamical systems and evolutionary variational inequalities. Eu J Oper Res (in press)

Dafermos S.C (1972) The traffic assignment problem for multiclass-user transportation networks. Transport Sci 6:73–87

Dafermos S (1980) Traffic equilibrium and variational inequalities. Transport Sci 14:42–54

Dafermos S (1982) The general multimodal network equilibrium problem with elastic demand. Networks 12:57–72

Dafermos S, Nagurney A (1984) Sensitivity analysis for the general spatial economic equilibrium problem. Oper Res 32:1069–1086

Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Nat Bureau Standards 73B:91–118

Daniele P (2003) Evolutionary variational inequalities and economic models for demand supply markets. Math Models Methods Appl Sci 4:471–489

Daniele P (2004) Time-dependent spatial price equilibrium problem: existence and stability results for the quantity formulation model. J Global Optimizat 28:283–295

Daniele P (2006) Dynamic networks and evolutionary variational inequalities. Edward Elgar Publishing, Cheltenham, England

Daniele P, Maugeri A, Oettli W (1999) Time-dependent variational inequalities. J Optimiz Theory Appl 103:543–555

El Azouzi R (2002) Avoiding paradox in routing games in networks when travel demand is elastic. In: Proceedings of the tenth symposium on dynamic games and applications. St. Petersburg, Russia

Florian M, Los M (1982) A new look at static spatial price equilibrium models. Reg Sci Urban Econ 12:579–597

Gallager RG (1977) A minimum delay routing algorithm using distributed computation. IEEE Trans Commun 25:73–85

Kinderlehrer D, Stampacchia G (1980) An introduction to variational inequalities and their applications. Academic Press, New York

Korilis YA, Lazar AA, Orda A (1999) Avoiding the Braess paradox in non-cooperative networks. J Appl Probab 36:211–222

Lions J.L, Stampacchia G (1967) Variational inequalities. Commun Pure Appl Math 22:493–519

Nagurney A (1989) Migration equilibrium and variational inequalities. Econ Lett 31:109–112

Nagurney A (1993) Network economics: A variational inequality approach. Kluwer Academic Publishers, Dordrecht

Nagurney A (2006) Supply chain network economics: Dynamics of prices, flows, and profits. Edward Elgar Publishing, Cheltenham, England

Nagurney A, Dong J (2002) Supernetworks: Decision-making for the Information Age. Edward Elgar Publishing, Cheltenham, England

Nagurney A, Liu Z, Cojocaru M-G, Daniele P (2006) Static and dynamic transportation network equilibrium reformulations of electric power supply chain networks with known demands. Transport Res E (in press)

Nagurney A, Siokos S (1997) Financial networks: Statics and dynamics. Springer, Berlin Heidelberg New York

Pas EI, Principio SL (1997) Braess paradox: some new insights. Transport Res B 31:265–276

Ran B, Boyce DE (1996) Modeling dynamic transportation networks. Springer, Berlin Heidelberg New York

Resende MGC, Pardalos PM (eds) (2006) Handbook of optimization in telecommunications. Springer Science and Business Media, New York

Roughgarden T (2005) Selfish routing and the price of anarchy. MIT Press, Cambridge, MA

Smith M (1979) Existence, uniquness, and stability of traffic equilibria. Transport Res B 13: 259–304

Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc Inst Civil Eng Part II, pp 325–378

Zhao L, Dafermos S (1991) General economic equilibrium and variational inequalities. Oper Res Lett 10:369–376