Aashtiani, H.Z., and T.L. Magnanti (1981).Equilibria on a congested transportation network. SIAM J. Algebraic and Discrete Methods2, 213–226.
Beckmann, M., C.B. McGuire and C.B. Winsten (1956).Studies in the Economics of Transportation. Yale University Press, New Haven CT.
Bertsekas, D.P. and E.M. Gafni (1982).Projection methods for variational inequalities with application to the traffic assignment problem. Mathematical Programming Study17, 139–159.
Bureau of Public Roads (1964).Traffic Assignment Manual. U.S. Department of Commerce, Urban Planning Division, Washington, DC.
Dafermos, S.C. (1980).Traffic assignment and variational inequalities. Transportation Science14 (1), 42–54.
Dafermos, S.C. (1982).Relaxation algorithms for the general asymmetric traffic equilibrium problem. Transportation Science16 (2), 231–240.
Dafermos, S.C. (1983).An iterative scheme for variational inequalities. Mathematical Programming26 (1), 40–47.
Deo, N. and C. Pang (1984).Shortest-path algorithms: taxonomy and annotation. Networks Vol14, 275–323.
Fisk, C. and S. Nguyen (1982).Solution algorithms for network equilibrium models with asymmetric user costs. Transp. Sci.16 (3), 361–381.
Florian, M. and H. Spiess (1982).The convergence of diagonalization algorithms for asymmetric network equilibrium problems. Trans. Res.16B (6), 447–483.
Florian, M. (1986).Nonlinear Cost Network Models in Transportation Analysis. Mathematical Programming Study26, 167–196.
Frank, M. and P. Wolfe (1956).An algorithm for quadratic programming. Naval Research Logistics Quarterly3, 95–110.
Gallo, G. and S. Pallotino (1984).Shortest Path Methods in Transportation Models. In Transportation Planning Models (Edited by M. Florian), 227–256. Elsevier, New York.
Gill, P.E., W. Murray and M. Wright (1981). Practical Optimization. Academic Press.
Harker, P. and J. Pang (1990).Finite-dimensional variational inequality and linear complementary problems: a survey of theory, algorithms and applications
. Mathematical Programming48
Hearn, D.W. (1982).The gap function of a convex program
. Oper. Res. Lett.1
Hohenbalken, B. (1977).Simplicial Decomposition in Nonlinear Programming algorithms
. Mathematical Programming13
Holloway, C.A. (1974).An extension of the Frank and Wolfe method of feasible directions
. Mathematical Programming,6
Kinderlehrer, D. and G. Stampacchia (1980).An Introduction to Variational Inequalities and Their Applications. Academic, New York.
Knuth, D.E. (1973).The Art of Computer Programming. Addison-Wesley.
Larsson, T. and M. Patriksson (1992).A dual scheme for traffic assignment problems
. Transportation Science26
Lawphongpanich, S. and D.W. Hearn (1984).Simplicial decomposition of the asymmetric traffic assignment problem
. Transp. Res18B
Luenberger, D.G. (1974).Introduction to Linear and Nonlinear Programming. Addison-Wesley, Reading, MA.
Magnanti, T.L. (1984).Models and Algorithms for Predicting Urban Traffic Equilibria. In Transportation Planning Models (Edited by M. Florian), 153–186, Elsevier, New York.
Marcotte, P. and J.P. Dussault (1987).A note on a globally convergent Newton method for solving monotone variational inequalities
. Operations Research Letters6
, No 1, 35–42.CrossRef
Marcotte P. and J. Guélat (1988).Adaptation of a modified Newton method for solving the asymmetric traffic equilibrium problem. Transportation Science,22, 112–124.
Montero L. (1992).A Simplicial Decomposition Approach for Solving the Variational Inequality Formulation of the General Traffic Assignment Problem for Large Scale Networks. Ph.D. Thesis supervised by Professor Jaume Barceló, Politechnical University of Catalunya in Barcelona (Spain).
Nguyen, S. and C. Depuis (1984).An efficient method for computing traffic equilibria in network with asymmetric transportation costs. Transp.
Pang, J.S. and D. Chan (1982).Iterative Methods for variational and complementary problems
. Mathematical Programming24
Pang, J.S. and C.S. Yu (1984).Linearized simplicial decomposition methods for computing traffic equilibria on networks. Networks14 (3), 427–438.
Patriksson, M. (1990).The traffic assignment problem. Theory and Algorithms Report LiTH-MAT-R-90-29, Department of Mathematics, Institute of Technology, Linköping University, Sweden.
Sheffi, Y. (1985). Urban transportation networks. Equilibrium analysis with mathematical methods. Prentice Hall, Englewood Cliffs, New Jersey.
Smith, M.J. (1979b).Existence, uniqueness and stability of traffic equilibria
. Transp. Res.13B
Smith, M.J. (1981a).The existence of an equilibrium solution, to the traffic assignment problem when there are junction interactions
. Transportation Research B,15B
No 6, 443–451.CrossRef
Smith, M.J. (1981b).Properties of a traffic control policy which ensure the existence of a traffic equilibrium consistent with the policy
. Transportation Research B,15B
No 6, 453–462.CrossRef
Smith, M.J. (1983a).The existence and calculation of traffic equilibria
. Transp. Res.17B
Smith, M.J. (1983b).Art algorithm for solving asymmetric equilibrium problems with continuous cost-flow function
. Transp. Res.17B
Smith, M.J. (1985).Traffic Signals in assignment
. Transportation Research B,19B
, No 2, 155–160.CrossRef
Smith, M.J., and M. Ghali (1989).The interaction between traffic flow and traffic control in congested urban networks. Paper for the Italian/USA Traffic Conference, Naples.
Wardrop, J.G. (1952).Some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. Part II,1 (2), 325–378.