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

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Abstract

In this paper, we develop an evolutionary variational inequality model of the Internet with multiple classes of traffic and demonstrate its utility through the formulation and solution of a time-dependent Braess paradox. The model can handle time-dependent changes in demand as a consequence of developing news stories, following, for example, natural disasters or catastrophes or major media events. The model can also capture the time-varying demand for Internet resources during a regular weekday with its more regular rhythm of work and breaks. In addition, the model includes time-varying capacities on the route flows due to, for example, government interventions or network-type failures.

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References

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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

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Correspondence to Anna Nagurney.

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Nagurney, A., Parkes, D. & Daniele, P. The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox. CMS 4, 355–375 (2007). https://doi.org/10.1007/s10287-006-0027-7

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