The Prevalence of Paradoxes in Transportation Equilibrium Problems

Consider a congested transportation network, where the cost along each arc is affine, i.e., consists of a fixed cost plus a variable cost proportional to the flow. We present a new paradox demonstrating that, in a congested transportation network, a sufficiently high increase in the congestion effect along a route can result in the abandonment of a different route having the same origin and destination while the original route continues to be used. We also present a method for testing whether or not the paradox will occur in an arbitrary transportation network by viewing the question as a parametric linear complementarity problem. The new paradox is contrasted with Braess' paradox, and intuition is developed to explain the prevalence of such paradoxes in transportation equilibrium problems.

[1]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

[2]  Stella Dafermos,et al.  An iterative scheme for variational inequalities , 1983, Math. Program..

[3]  Terry L. Friesz,et al.  TRANSPORTATION NETWORK EQUILIBRIUM, DESIGN AND AGGREGATION: KEY DEVELOPMENTS AND RESEARCH OPPORTUNITIES. IN: THE AUTOMOBILE , 1985 .

[4]  C. Fisk.  More paradoxes in the equilibrium assignment problem , 1979 .

[5]  Anna Nagurney,et al.  Sensitivity analysis for the asymmetric network equilibrium problem , 1984, Math. Program..

[6]  J. D. Murchland,et al.  Braess's paradox of traffic flow , 1970 .

[7]  R. Cottle.  Manifestations of the Schur complement , 1974 .

[8]  C. B. Mcguire,et al.  Studies in the Economics of Transportation , 1958 .

[9]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[10]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[11]  Dietrich Braess,et al.  Über ein Paradoxon aus der Verkehrsplanung , 1968, Unternehmensforschung.

[12]  A. Nagurney,et al.  ON SOME TRAFFIC EQUILIBRIUM THEORY PARADOXES , 1984 .

[13]  Marguerite FRANK,et al.  The Braess paradox , 1981, Math. Program..

[14]  T. Magnanti,et al.  Equilibria on a Congested Transportation Network , 1981 .

[15]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[16]  Shantayanan Devarajan,et al.  A note of network equilibrium and noncooperative games , 1981 .

[17]  Larry J. LeBlanc,et al.  An Algorithm for the Discrete Network Design Problem , 1975 .

[18]  R. Asmuth.  Traffic network equilibria , 1978 .

[19]  Richard Steinberg,et al.  PREVALENCE OF BRAESS' PARADOX , 1983 .

[20]  M. A. Hall,et al.  Properties of the Equilibrium State in Transportation Networks , 1978 .

[21]  M. S. Bazaraa,et al.  Nonlinear Programming , 1979 .