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Volumn 8, Issue C, 1995, Pages 485-550

Chapter 6 Network Equilibrium Models and Algorithms

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EID: 77957094045     PISSN: 09270507     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0927-0507(05)80110-0     Document Type: Review
Times cited : (164)

References (227)
  • 3
    • 0018535505 scopus 로고
    • Methods for combining modal split and equilibrium assignment models
    • Abdulaal, M., LeBlanc, L.J., Methods for combining modal split and equilibrium assignment models. Transp. Sci. 13 (1979), 292–314.
    • (1979) Transp. Sci. , vol.13 , pp. 292-314
    • Abdulaal, M.1    LeBlanc, L.J.2
  • 4
    • 0007924913 scopus 로고
    • Computation of Market Equilibria for Policy Analysis: the Project Independence Evaluation Systems (PIES) Approach
    • Garland Kansas City, Mo.
    • Ahn, B.-H., Computation of Market Equilibria for Policy Analysis: the Project Independence Evaluation Systems (PIES) Approach. 1979, Garland, Kansas City, Mo.
    • (1979)
    • Ahn, B.-H.1
  • 5
    • 0002631476 scopus 로고
    • On convergence of the PIES algorithm for computing equilibria
    • Ahn, B.-H., Hogan, W.W., On convergence of the PIES algorithm for computing equilibria. Oper. Res. 30 (1982), 281–300.
    • (1982) Oper. Res. , vol.30 , pp. 281-300
    • Ahn, B.-H.1    Hogan, W.W.2
  • 6
    • 0025383068 scopus 로고
    • A full analytical implementation of the PARTAN/Frank-Wolfe algorithm for equilibrium assignment
    • Arezki, Y., Van Vliet, D., A full analytical implementation of the PARTAN/Frank-Wolfe algorithm for equilibrium assignment. Transp. Sci. 24 (1990), 58–62.
    • (1990) Transp. Sci. , vol.24 , pp. 58-62
    • Arezki, Y.1    Van Vliet, D.2
  • 7
    • 0004170297 scopus 로고
    • Traffic network equilibria
    • Stanford University New York, NY
    • Asmuth, R., Traffic network equilibria. Ph.D. dissertation, 1978, Stanford University, New York, NY.
    • (1978) Ph.D. dissertation
    • Asmuth, R.1
  • 8
    • 0017938095 scopus 로고
    • Multicommodity network flow — a survey
    • Assad, A.A., Multicommodity network flow — a survey. Networks 8 (1978), 37–91.
    • (1978) Networks , vol.8 , pp. 37-91
    • Assad, A.A.1
  • 9
    • 0024739313 scopus 로고
    • Variational principles for variational inequalities
    • Auchmuty, G., Variational principles for variational inequalities. Numer. Funct. Anal. Optim. 10 (1989), 863–874.
    • (1989) Numer. Funct. Anal. Optim. , vol.10 , pp. 863-874
    • Auchmuty, G.1
  • 10
    • 0002183298 scopus 로고
    • Optimisation. Méthodes Numériques
    • Masson Stanford, CA
    • Auslender, A., Optimisation. Méthodes Numériques. 1976, Masson, Stanford, CA.
    • (1976)
    • Auslender, A.1
  • 11
    • 2142711968 scopus 로고
    • EMME/2: Interactive graphic method for road and transit planning
    • Babin, A., Florian, M., James-Lefebvre, L., Spiess, H., EMME/2: Interactive graphic method for road and transit planning. Transp. Res. Rec. 866 (1982), 1–9.
    • (1982) Transp. Res. Rec. , vol.866 , pp. 1-9
    • Babin, A.1    Florian, M.2    James-Lefebvre, L.3    Spiess, H.4
  • 12
    • 23144436176 scopus 로고
    • On the equivalence of transfer and generalized Benders decomposition
    • Barton, R.R., Hearn, D.W., Ribera, J., On the equivalence of transfer and generalized Benders decomposition. Transp. Res. 23B (1989), 61–73.
    • (1989) Transp. Res. , vol.23B , pp. 61-73
    • Barton, R.R.1    Hearn, D.W.2    Ribera, J.3
  • 13
    • 84927765685 scopus 로고
    • Nonlinear programming, theory and algorithms
    • John Wiley & Sons, Inc. Paris
    • Bazaraa, M.S., Shetty, C.M., Nonlinear programming, theory and algorithms. 1979, John Wiley & Sons, Inc., Paris.
    • (1979)
    • Bazaraa, M.S.1    Shetty, C.M.2
  • 14
    • 33747058886 scopus 로고
    • On the theory of traffic flow in networks
    • Beckmann, M.J., On the theory of traffic flow in networks. Traffic Q. 21 (1967), 109–117.
    • (1967) Traffic Q. , vol.21 , pp. 109-117
    • Beckmann, M.J.1
  • 15
    • 0003625346 scopus 로고
    • Studies in the Economics of Transportation
    • Yale University Press NY
    • Beckmann, M., McGuire, C.B., Winsten, C.B., Studies in the Economics of Transportation. 1956, Yale University Press, NY.
    • (1956)
    • Beckmann, M.1    McGuire, C.B.2    Winsten, C.B.3
  • 16
    • 0016948909 scopus 로고
    • On the Goldstein-Levitin-Polyak gradient projection method
    • Bertsekas, D.P., On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Automatic Control AC-21 (1976), 174–184.
    • (1976) IEEE Trans. Automatic Control , vol.AC-21 , pp. 174-184
    • Bertsekas, D.P.1
  • 17
    • 0012357926 scopus 로고
    • Algorithms for nonlinear multicommodity network flow problems
    • A. Bensoussan J.L. Lions Springer-Verlag New Haven, CT
    • Bertsekas, D.P., Algorithms for nonlinear multicommodity network flow problems. Bensoussan, A., Lions, J.L., (eds.) Proceedings of the International Symposium on Systems Optimization and Analysis, 1979, Springer-Verlag, New Haven, CT, 210–224.
    • (1979) Proceedings of the International Symposium on Systems Optimization and Analysis , pp. 210-224
    • Bertsekas, D.P.1
  • 19
    • 0000377218 scopus 로고
    • Projected Newton methods for optimization problems with simple constraints
    • Bertsekas, D.P., Projected Newton methods for optimization problems with simple constraints. SIAM J. Control Optim. 20 (1982), 221–246.
    • (1982) SIAM J. Control Optim. , vol.20 , pp. 221-246
    • Bertsekas, D.P.1
  • 20
    • 0000050153 scopus 로고
    • Projection methods for variational inequalities with application to the traffic assignment problem
    • Bertsekas, D.P., Gafni, E.M., Projection methods for variational inequalities with application to the traffic assignment problem. Math. Program. Study 17 (1982), 139–159.
    • (1982) Math. Program. Study , vol.17 , pp. 139-159
    • Bertsekas, D.P.1    Gafni, E.M.2
  • 21
    • 84946968804 scopus 로고
    • Data Communication Networks
    • Prentice-Hall NY
    • Bertsekas, D.P., Gallager, R.G., Data Communication Networks. 1987, Prentice-Hall, NY.
    • (1987)
    • Bertsekas, D.P.1    Gallager, R.G.2
  • 22
    • 80053030329 scopus 로고
    • Implementation of an optimal multicommodity network flow algorithm based on gradient projection and a path flow formulation
    • Laboratory for Information and Decision Studies, Massachusetts Institute of Technology Englewood Cliffs, NJ
    • Bertsekas, D.P., Gendron, B., Tsai, W.K., Implementation of an optimal multicommodity network flow algorithm based on gradient projection and a path flow formulation. Technical Report LIDS-P-1364, 1984, Laboratory for Information and Decision Studies, Massachusetts Institute of Technology, Englewood Cliffs, NJ.
    • (1984) Technical Report LIDS-P-1364
    • Bertsekas, D.P.1    Gendron, B.2    Tsai, W.K.3
  • 23
    • 0003636164 scopus 로고
    • Parallel and Distributed Computation. Numerical Methods
    • Prentice-Hall Cambridge, MA
    • Bertsekas, D.P., Tsitsiklis, J.N., Parallel and Distributed Computation. Numerical Methods. 1989, Prentice-Hall, Cambridge, MA.
    • (1989)
    • Bertsekas, D.P.1    Tsitsiklis, J.N.2
  • 24
    • 0000503918 scopus 로고
    • Urban transportation network-equilibrium and design models: recent achievements and future prospects
    • Boyce, D.E., Urban transportation network-equilibrium and design models: recent achievements and future prospects. Environ. Plann. 16A (1984), 1445–1474.
    • (1984) Environ. Plann. , vol.16A , pp. 1445-1474
    • Boyce, D.E.1
  • 25
    • 0024158360 scopus 로고
    • Network equilibrium models for urban location and travel choices: a retrospective survey
    • Boyce, D.E., LeBlanc, L.J., Chou, K.S., Network equilibrium models for urban location and travel choices: a retrospective survey. J. Region. Sci. 28 (1988), 159–183.
    • (1988) J. Region. Sci. , vol.28 , pp. 159-183
    • Boyce, D.E.1    LeBlanc, L.J.2    Chou, K.S.3
  • 26
    • 34250513249 scopus 로고
    • Über ein Paradoxen der Verkehrsplannung
    • Braess, D., Über ein Paradoxen der Verkehrsplannung. Unternehmenforschung 12 (1968), 258–268.
    • (1968) Unternehmenforschung , vol.12 , pp. 258-268
    • Braess, D.1
  • 27
    • 0018433532 scopus 로고
    • On the existence of equilibria in asymmetrical multiclass-user transportation networks
    • Braess, D., Koch, G., On the existence of equilibria in asymmetrical multiclass-user transportation networks. Transp. Sci. 13 (1979), 56–63.
    • (1979) Transp. Sci. , vol.13 , pp. 56-63
    • Braess, D.1    Koch, G.2
  • 28
    • 0002411072 scopus 로고
    • Une méthode d'affectation du trafic
    • Beiträge zur Theorie des Verkehrsflusses Strassenbau und Strassenverkehrstechnik Heft 86 W. Lentzback P. Baron Karlsruhe, 1968 Herausgeben von Bundesminister fur Verkehr, Abteilung Strassenbau Englewood Cliffs, NJ
    • Beiträge zur Theorie des Verkehrsflusses Strassenbau und Strassenverkehrstechnik Heft 86 Bruynooghe, M., Gibert, A., Sakarovitch, M., Une méthode d'affectation du trafic. Lentzback, W., Baron, P., (eds.) Fourth International Symposium on the Theory of Traffic Flow, Karlsruhe, 1968, 1969, Herausgeben von Bundesminister fur Verkehr, Abteilung Strassenbau, Englewood Cliffs, NJ, 198–204.
    • (1969) Fourth International Symposium on the Theory of Traffic Flow , pp. 198-204
    • Bruynooghe, M.1    Gibert, A.2    Sakarovitch, M.3
  • 29
    • 0011917342 scopus 로고
    • Multipath route assignment and its application to capacity restraint
    • Beiträge zur Theorie des Verkehrsflusses Strassenbau und Strassenverkehrstechnik Heft 86 W. Lentzback P. Baron Karlsruhe, 1968 Herausgeben von Bundesminister fur Verkehr, Abteilung Strassenbau Bonn
    • Burrell, J.E., Multipath route assignment and its application to capacity restraint. Lentzback, W., Baron, P., (eds.) Fourth International Symposium on the Theory of Traffic Flow, Karlsruhe, 1968 Beiträge zur Theorie des Verkehrsflusses Strassenbau und Strassenverkehrstechnik Heft 86, 1969, Herausgeben von Bundesminister fur Verkehr, Abteilung Strassenbau, Bonn.
    • (1969) Fourth International Symposium on the Theory of Traffic Flow
    • Burrell, J.E.1
  • 31
    • 0009960666 scopus 로고
    • A tight upper bound on the rate of convergence of the Frank-Wolfe algorithm
    • Canon, M.D., Cullum, C.D., A tight upper bound on the rate of convergence of the Frank-Wolfe algorithm. SIAM J. Control 6 (1968), 509–516.
    • (1968) SIAM J. Control , vol.6 , pp. 509-516
    • Canon, M.D.1    Cullum, C.D.2
  • 32
    • 0016115384 scopus 로고
    • Optimal routing in a packet switched network
    • Cantor, D.G., Gerla, M., Optimal routing in a packet switched network. IEEE Trans. Comput. C-23 (1974), 1062–1069.
    • (1974) IEEE Trans. Comput. , vol.C-23 , pp. 1062-1069
    • Cantor, D.G.1    Gerla, M.2
  • 33
    • 0022268503 scopus 로고
    • The dual of the traffic assignment problem with elastic demands
    • Carey, M., The dual of the traffic assignment problem with elastic demands. Transp. Res. 19B (1985), 227–237.
    • (1985) Transp. Res. , vol.19B , pp. 227-237
    • Carey, M.1
  • 34
    • 0021645081 scopus 로고
    • Spatial price equilibrium sensitivity analysis
    • Chao, G.S., Friesz, T.L., Spatial price equilibrium sensitivity analysis. Trans. Res. 18B (1984), 423–440.
    • (1984) Trans. Res. , vol.18B , pp. 423-440
    • Chao, G.S.1    Friesz, T.L.2
  • 36
    • 11244284340 scopus 로고
    • Multicopy traffic network models
    • R. Herman Elsevier Berlin
    • Charnes, A., Cooper, W.W., Multicopy traffic network models. Herman, R., (eds.) Theory of Traffic Flow, 1961, Elsevier, Berlin, 85–96.
    • (1961) Theory of Traffic Flow , pp. 85-96
    • Charnes, A.1    Cooper, W.W.2
  • 37
    • 0039588616 scopus 로고
    • Solving the pipe network analysis problem using optimization techniques
    • Collins, M., Cooper, L., Helgason, R., Kennington, J., LeBlanc, L., Solving the pipe network analysis problem using optimization techniques. Manage. Sci. 24 (1978), 747–760.
    • (1978) Manage. Sci. , vol.24 , pp. 747-760
    • Collins, M.1    Cooper, L.2    Helgason, R.3    Kennington, J.4    LeBlanc, L.5
  • 38
    • 0017823783 scopus 로고
    • Solution of large scale pipe networks by improved mathematical approaches
    • School of Engineering and Applied Science, Southern Methodist University Amsterdam
    • Collins, M., Cooper, L., Helgason, R., Kennington, J., Solution of large scale pipe networks by improved mathematical approaches. IEOR Report 77016-WR77001, 1978, School of Engineering and Applied Science, Southern Methodist University, Amsterdam.
    • (1978) IEOR Report 77016-WR77001
    • Collins, M.1    Cooper, L.2    Helgason, R.3    Kennington, J.4
  • 39
    • 0015160527 scopus 로고
    • An extended traffic assignment model with applications to two-way traffic
    • Dafermos, S., An extended traffic assignment model with applications to two-way traffic. Transp. Sci. 5 (1971), 366–389.
    • (1971) Transp. Sci. , vol.5 , pp. 366-389
    • Dafermos, S.1
  • 40
    • 0015300502 scopus 로고
    • The traffic assignment problem for multiclass-user transportation networks
    • Dafermos, S., The traffic assignment problem for multiclass-user transportation networks. Transp. Sci. 6 (1972), 73–87.
    • (1972) Transp. Sci. , vol.6 , pp. 73-87
    • Dafermos, S.1
  • 41
    • 0015655088 scopus 로고
    • Toll patterns for multi-class user transportation networks
    • Dafermos, S., Toll patterns for multi-class user transportation networks. Transp. Sci. 7 (1973), 211–223.
    • (1973) Transp. Sci. , vol.7 , pp. 211-223
    • Dafermos, S.1
  • 42
    • 0002036820 scopus 로고
    • Traffic equilibrium and variational inequalities
    • Dafermos, S., Traffic equilibrium and variational inequalities. Transp. Sci. 14 (1980), 42–54.
    • (1980) Transp. Sci. , vol.14 , pp. 42-54
    • Dafermos, S.1
  • 43
    • 0020097715 scopus 로고
    • The general multimodal network equilibrium problem with elastic demand
    • Dafermos, S., The general multimodal network equilibrium problem with elastic demand. Networks 12 (1982), 57–72.
    • (1982) Networks , vol.12 , pp. 57-72
    • Dafermos, S.1
  • 44
    • 0020125717 scopus 로고
    • Relaxation algorithms for the general asymmetric traffic equilibrium problem
    • Dafermos, S., Relaxation algorithms for the general asymmetric traffic equilibrium problem. Transp. Sci. 16 (1982), 231–240.
    • (1982) Transp. Sci. , vol.16 , pp. 231-240
    • Dafermos, S.1
  • 45
    • 0020748950 scopus 로고
    • An iterative scheme for variational inequalities
    • Dafermos, S., An iterative scheme for variational inequalities. Math. Program. 26 (1983), 40–47.
    • (1983) Math. Program. , vol.26 , pp. 40-47
    • Dafermos, S.1
  • 46
    • 0001707277 scopus 로고
    • Sensitivity analysis in variational inequalities
    • Dafermos, S., Sensitivity analysis in variational inequalities. Math. Oper. Res. 13 (1988), 421–434.
    • (1988) Math. Oper. Res. , vol.13 , pp. 421-434
    • Dafermos, S.1
  • 47
    • 0021489890 scopus 로고
    • Sensitivity analysis for the general spatial economic equilibrium problem
    • Dafermos, S., Nagurney, A., Sensitivity analysis for the general spatial economic equilibrium problem. Oper. Res. 32 (1984), 1069–1086.
    • (1984) Oper. Res. , vol.32 , pp. 1069-1086
    • Dafermos, S.1    Nagurney, A.2
  • 48
    • 0021371581 scopus 로고
    • Sensitivity analysis for the asymmetric network equilibrium problem
    • Dafermos, S., Nagurney, A., Sensitivity analysis for the asymmetric network equilibrium problem. Math. Program. 28 (1984), 174–184.
    • (1984) Math. Program. , vol.28 , pp. 174-184
    • Dafermos, S.1    Nagurney, A.2
  • 49
    • 0021405975 scopus 로고
    • On some traffic equilibrium theory paradoxes
    • Dafermos, S., Nagurney, A., On some traffic equilibrium theory paradoxes. Trans. Res. 18B (1984), 101–110.
    • (1984) Trans. Res. , vol.18B , pp. 101-110
    • Dafermos, S.1    Nagurney, A.2
  • 50
    • 0003104807 scopus 로고
    • Stability and sensitivity analysis for the general network equilibrium-travel choice model
    • J. Volmuller R. Hamerslag Delft VNU Science Press Utrecht
    • Dafermos, S., Nagurney, A., Stability and sensitivity analysis for the general network equilibrium-travel choice model. Volmuller, J., Hamerslag, R., (eds.) Proceedings of the Ninth International Symposium on Transportation and Traffic Theory, Delft, 1984, VNU Science Press, Utrecht, 217–231.
    • (1984) Proceedings of the Ninth International Symposium on Transportation and Traffic Theory , pp. 217-231
    • Dafermos, S.1    Nagurney, A.2
  • 51
    • 5244381169 scopus 로고
    • Isomorphism between spatial price and traffic equilibrium models
    • Lefschetz Center for Dynamical Systems, Brown University Utrecht
    • Dafermos, S., Nagurney, A., Isomorphism between spatial price and traffic equilibrium models. Report LCDS #85-17, 1985, Lefschetz Center for Dynamical Systems, Brown University, Utrecht.
    • (1985) Report LCDS #85-17
    • Dafermos, S.1    Nagurney, A.2
  • 52
    • 0008769233 scopus 로고
    • Supply and demand equilibration algorithms for a class of market equilibrium problems
    • Dafermos, S., Nagurney, A., Supply and demand equilibration algorithms for a class of market equilibrium problems. Transp. Sci. 23 (1989), 118–124.
    • (1989) Transp. Sci. , vol.23 , pp. 118-124
    • Dafermos, S.1    Nagurney, A.2
  • 53
    • 0014491807 scopus 로고
    • The traffic assignment problem for a general network
    • Dafermos, S., Sparrow, F.T., The traffic assignment problem for a general network. J. Res. Nat. Bur. Stand. 73B (1969), 91–118.
    • (1969) J. Res. Nat. Bur. Stand. , vol.73B , pp. 91-118
    • Dafermos, S.1    Sparrow, F.T.2
  • 54
    • 0001002832 scopus 로고
    • Optimal resource allocation and toll patterns in user-optimised transport networks
    • Dafermos, S., Sparrow, F.T., Optimal resource allocation and toll patterns in user-optimised transport networks. J. Trans. Econ. Policy 5 (1971), 184–200.
    • (1971) J. Trans. Econ. Policy , vol.5 , pp. 184-200
    • Dafermos, S.1    Sparrow, F.T.2
  • 55
    • 49449122944 scopus 로고
    • On the traffic assignment problem with flow dependent costs — 1
    • Daganzo, C.F., On the traffic assignment problem with flow dependent costs — 1. Trans. Res. 11 (1977), 433–437.
    • (1977) Trans. Res. , vol.11 , pp. 433-437
    • Daganzo, C.F.1
  • 56
    • 49449123935 scopus 로고
    • On the traffic assignment problem with flow dependent costs — 2
    • Daganzo, C.F., On the traffic assignment problem with flow dependent costs — 2. Trans. Res. 11 (1977), 439–441.
    • (1977) Trans. Res. , vol.11 , pp. 439-441
    • Daganzo, C.F.1
  • 57
    • 0020168223 scopus 로고
    • Unconstrained extremal formulations of some transportation equilibrium problems
    • Daganzo, C.F., Unconstrained extremal formulations of some transportation equilibrium problems. Transp. Sci. 16 (1982), 332–360.
    • (1982) Transp. Sci. , vol.16 , pp. 332-360
    • Daganzo, C.F.1
  • 58
    • 0020807080 scopus 로고
    • Stochastic network equilibrium with multiple vehicle types and asymmetric, indefinite link cost Jacobians
    • Daganzo, C.F., Stochastic network equilibrium with multiple vehicle types and asymmetric, indefinite link cost Jacobians. Transp. Sci. 17 (1983), 282–300.
    • (1983) Transp. Sci. , vol.17 , pp. 282-300
    • Daganzo, C.F.1
  • 59
    • 0017525664 scopus 로고
    • On stochastic models of traffic assignment
    • Daganzo, C.F., Sheffi, Y., On stochastic models of traffic assignment. Transp. Sci. 11 (1977), 253–274.
    • (1977) Transp. Sci. , vol.11 , pp. 253-274
    • Daganzo, C.F.1    Sheffi, Y.2
  • 60
    • 11244304006 scopus 로고
    • The application of decomposition to transportation networks analysis
    • U.S. Department of Transportation Providence, RI
    • Dantzig, G.B., Maier, S.F., Lansdowne, Z.F., The application of decomposition to transportation networks analysis. Report DOT-TSC-OST-76-26, 1976, U.S. Department of Transportation, Providence, RI.
    • (1976) Report DOT-TSC-OST-76-26
    • Dantzig, G.B.1    Maier, S.F.2    Lansdowne, Z.F.3
  • 61
    • 0023410249 scopus 로고
    • A primal truncated Newton algorithm with application to large-scale nonlinear network optimization
    • Dembo, R.S., A primal truncated Newton algorithm with application to large-scale nonlinear network optimization. Math. Program. Study 31 (1987), 43–71.
    • (1987) Math. Program. Study , vol.31 , pp. 43-71
    • Dembo, R.S.1
  • 62
    • 0019670630 scopus 로고
    • A scale reduced gradient algorithm for network flow problems with convex separable costs
    • Dembo, R.S., Klincewicz, J.G., A scale reduced gradient algorithm for network flow problems with convex separable costs. Math. Program. Study 15 (1981), 125–147.
    • (1981) Math. Program. Study , vol.15 , pp. 125-147
    • Dembo, R.S.1    Klincewicz, J.G.2
  • 63
    • 84987047941 scopus 로고
    • Computing equilibria on large multicommodity networks: an application of truncated quadratic programming algorithms
    • Dembo, R.S., Tulowitzki, U., Computing equilibria on large multicommodity networks: an application of truncated quadratic programming algorithms. Networks 18 (1988), 273–284.
    • (1988) Networks , vol.18 , pp. 273-284
    • Dembo, R.S.1    Tulowitzki, U.2
  • 64
    • 0002776326 scopus 로고
    • Mathematical programming and electrical networks
    • MIT Press and John Wiley Washington, D.C.
    • Dennis, J.B., Mathematical programming and electrical networks. 1959, MIT Press and John Wiley, Washington, D.C.
    • (1959)
    • Dennis, J.B.1
  • 65
    • 0015078345 scopus 로고
    • A probabilistic multipath traffic assignment model which obviates path enumeration
    • Dial, R.B., A probabilistic multipath traffic assignment model which obviates path enumeration. Trans. Res. 5 (1971), 83–111.
    • (1971) Trans. Res. , vol.5 , pp. 83-111
    • Dial, R.B.1
  • 66
    • 0018482045 scopus 로고
    • Capacity restrained road assignment
    • Dow, P., Van Vliet, D., Capacity restrained road assignment. Traffic Eng. Control 20 (1979), 296–305.
    • (1979) Traffic Eng. Control , vol.20 , pp. 296-305
    • Dow, P.1    Van Vliet, D.2
  • 67
    • 84985234252 scopus 로고
    • An algorithm for the spatial price equilibrium problem on a general network in the space of path flows
    • Drissi-Kaïtouni, O., Florian, M., An algorithm for the spatial price equilibrium problem on a general network in the space of path flows. J. Region. Sci. 31 (1991), 171–190.
    • (1991) J. Region. Sci. , vol.31 , pp. 171-190
    • Drissi-Kaïtouni, O.1    Florian, M.2
  • 68
    • 0022764149 scopus 로고
    • The convergence conditions of diagonalization and projection methods for fixed demand asymmetric network equilibrium problems
    • Dupuis, C., Darveau, J.-M., The convergence conditions of diagonalization and projection methods for fixed demand asymmetric network equilibrium problems. Oper. Res. Lett. 5 (1986), 149–155.
    • (1986) Oper. Res. Lett. , vol.5 , pp. 149-155
    • Dupuis, C.1    Darveau, J.-M.2
  • 69
    • 0018698665 scopus 로고
    • On the calibration of the combined distribution-assignment model
    • Erlander, S., Nguyen, S., Stewart, N., On the calibration of the combined distribution-assignment model. Trans. Res. 13B (1979), 259–267.
    • (1979) Trans. Res. , vol.13B , pp. 259-267
    • Erlander, S.1    Nguyen, S.2    Stewart, N.3
  • 70
    • 0016920939 scopus 로고
    • Derivation and analysis of some models for combining trip distribution and assignment
    • Evans, S.P., Derivation and analysis of some models for combining trip distribution and assignment. Trans. Res. 10 (1976), 37–57.
    • (1976) Trans. Res. , vol.10 , pp. 37-57
    • Evans, S.P.1
  • 71
    • 84936337466 scopus 로고
    • Traffic equilibria on multiclass-user transportation networks analysed via variational inequalities
    • Fang, S.-C., Traffic equilibria on multiclass-user transportation networks analysed via variational inequalities. Tamkang J. Math. 13 (1982), 1–9.
    • (1982) Tamkang J. Math. , vol.13 , pp. 1-9
    • Fang, S.-C.1
  • 72
    • 0016126095 scopus 로고
    • Minimum cost multicommodity circulation problems with convex arc-costs
    • Ferland, J.A., Minimum cost multicommodity circulation problems with convex arc-costs. Transp. Sci. 8 (1974), 355–360.
    • (1974) Transp. Sci. , vol.8 , pp. 355-360
    • Ferland, J.A.1
  • 73
    • 0020735358 scopus 로고
    • Equilibrium predictions in transportation markets: the state of the art
    • Fernandez, J.E., Friesz, T.L., Equilibrium predictions in transportation markets: the state of the art. Trans. Res. 17B (1983), 155–172.
    • (1983) Trans. Res. , vol.17B , pp. 155-172
    • Fernandez, J.E.1    Friesz, T.L.2
  • 74
    • 0018712829 scopus 로고
    • More paradoxes in the equilibrium assignment problem
    • Fisk, C., More paradoxes in the equilibrium assignment problem. Trans. Res. 13B (1979), 305–309.
    • (1979) Trans. Res. , vol.13B , pp. 305-309
    • Fisk, C.1
  • 75
    • 0019229288 scopus 로고
    • Some developments in equilibrium traffic assignment
    • Fisk, C., Some developments in equilibrium traffic assignment. Trans. Res. 14B (1980), 243–255.
    • (1980) Trans. Res. , vol.14B , pp. 243-255
    • Fisk, C.1
  • 76
    • 0020846035 scopus 로고
    • Alternative variational inequality formulations of the network equilibrium-travel choice problem
    • Fisk, C.S., Boyce, D.E., Alternative variational inequality formulations of the network equilibrium-travel choice problem. Transp. Sci. 17 (1983), 454–463.
    • (1983) Transp. Sci. , vol.17 , pp. 454-463
    • Fisk, C.S.1    Boyce, D.E.2
  • 77
    • 0019633051 scopus 로고
    • Existence and uniqueness properties of an asymmetric two-mode equilibrium model
    • Fisk, C., Nguyen, S., Existence and uniqueness properties of an asymmetric two-mode equilibrium model. Transp. Sci. 15 (1981), 318–328.
    • (1981) Transp. Sci. , vol.15 , pp. 318-328
    • Fisk, C.1    Nguyen, S.2
  • 78
    • 0020168222 scopus 로고
    • Solution algorithms for network equilibrium models with asymmetric user costs
    • Fisk, C., Nguyen, S., Solution algorithms for network equilibrium models with asymmetric user costs. Transp. Sci. 16 (1982), 361–381.
    • (1982) Transp. Sci. , vol.16 , pp. 361-381
    • Fisk, C.1    Nguyen, S.2
  • 79
    • 0019392389 scopus 로고
    • Empirical evidence for equilibrium paradoxes with implications for optimal planning strategies
    • Fisk, C., Pallottino, S., Empirical evidence for equilibrium paradoxes with implications for optimal planning strategies. Trans. Res. 15A (1981), 245–248.
    • (1981) Trans. Res. , vol.15A , pp. 245-248
    • Fisk, C.1    Pallottino, S.2
  • 80
    • 0142252992 scopus 로고
    • An improved linear approximation algorithm for the network equilibrium (packet switching) problem
    • Florian, M., An improved linear approximation algorithm for the network equilibrium (packet switching) problem. Proc. 1977 IEEE Conference on Decision and Control, New Orleans, TX, 1977, 812–818.
    • (1977) Proc. 1977 IEEE Conference on Decision and Control, New Orleans, TX , pp. 812-818
    • Florian, M.1
  • 81
    • 85023527451 scopus 로고
    • A traffic equilibrium model of travel by car and public transit modes
    • Florian, M., A traffic equilibrium model of travel by car and public transit modes. Transp. Sci. 8 (1976), 168–179.
    • (1976) Transp. Sci. , vol.8 , pp. 168-179
    • Florian, M.1
  • 82
    • 0018682701 scopus 로고
    • Validation and application of EMME: an equilibrium based two-mode urban transportation planning method
    • Florian, M., Chapleau, R., Nguyen, S., Achim, C., James-Lefebvre, L., Fisk, C., Validation and application of EMME: an equilibrium based two-mode urban transportation planning method. Trans. Res. Record 728 (1979), 14–22.
    • (1979) Trans. Res. Record , vol.728 , pp. 14-22
    • Florian, M.1    Chapleau, R.2    Nguyen, S.3    Achim, C.4    James-Lefebvre, L.5    Fisk, C.6
  • 83
    • 0042274493 scopus 로고
    • An introduction to network models used in transportation planning
    • M. Florian North-Holland NY
    • Floridan, M., An introduction to network models used in transportation planning. Florian, M., (eds.) Transp. Plann. Models, 1984, North-Holland, NY, 137–152.
    • (1984) Transp. Plann. Models , pp. 137-152
    • Floridan, M.1
  • 84
    • 0020722522 scopus 로고
    • Nonlinear cost network models in transportation analysis
    • Florian, M., Nonlinear cost network models in transportation analysis. Math. Program. Study 26 (1986), 167–196.
    • (1986) Math. Program. Study , vol.26 , pp. 167-196
    • Florian, M.1
  • 85
    • 84987046957 scopus 로고
    • An efficient implementation of the PARTAN variant of the linear approximation method for the network equilibrium problem
    • Florian, M., Guélat, J., Spiess, H., An efficient implementation of the PARTAN variant of the linear approximation method for the network equilibrium problem. Networks 17 (1987), 319–339.
    • (1987) Networks , vol.17 , pp. 319-339
    • Florian, M.1    Guélat, J.2    Spiess, H.3
  • 86
    • 0020404417 scopus 로고
    • A new look at static spatial price equilibrium problems
    • Florian, M., Los, M., A new look at static spatial price equilibrium problems. Region. Sci. Urban Econ. 12 (1982), 579–597.
    • (1982) Region. Sci. Urban Econ. , vol.12 , pp. 579-597
    • Florian, M.1    Los, M.2
  • 87
    • 0016128684 scopus 로고
    • A method for computing network equilibrium with elastic demands
    • Florian, M., Nguyen, S., A method for computing network equilibrium with elastic demands. Transp. Sci. 8 (1974), 321–332.
    • (1974) Transp. Sci. , vol.8 , pp. 321-332
    • Florian, M.1    Nguyen, S.2
  • 88
    • 0017017564 scopus 로고
    • An application and validation of equilibrium trip assignment methods
    • Florian, M., Nguyen, S., An application and validation of equilibrium trip assignment methods. Transp. Sci. 10 (1976), 374–390.
    • (1976) Transp. Sci. , vol.10 , pp. 374-390
    • Florian, M.1    Nguyen, S.2
  • 90
    • 0018004899 scopus 로고
    • A combined trip distribution modal split and trip assignment model
    • Florian, M., Nguyen, S., A combined trip distribution modal split and trip assignment model. Trans. Res. 12 (1978), 241–246.
    • (1978) Trans. Res. , vol.12 , pp. 241-246
    • Florian, M.1    Nguyen, S.2
  • 91
    • 0016473670 scopus 로고
    • On the combined distribution-assignment of traffic
    • Florian, M., Nguyen, S., Ferland, J., On the combined distribution-assignment of traffic. Transp. Sci. 9 (1975), 43–53.
    • (1975) Transp. Sci. , vol.9 , pp. 43-53
    • Florian, M.1    Nguyen, S.2    Ferland, J.3
  • 92
    • 0020452865 scopus 로고
    • The convergence of diagonalization algorithms for asymmetric network equilibrium problems
    • Florian, M., Spiess, H., The convergence of diagonalization algorithms for asymmetric network equilibrium problems. Trans. Res. 16B (1982), 477–483.
    • (1982) Trans. Res. , vol.16B , pp. 477-483
    • Florian, M.1    Spiess, H.2
  • 93
    • 0020704141 scopus 로고
    • On binary mode choice/assignment models
    • Florian, M., Spiess, H., On binary mode choice/assignment models. Transp. Sci. 17 (1983), 32–47.
    • (1983) Transp. Sci. , vol.17 , pp. 32-47
    • Florian, M.1    Spiess, H.2
  • 94
    • 0019564259 scopus 로고
    • The Braess paradox
    • Frank, M., The Braess paradox. Math. Program. 20 (1981), 283–302.
    • (1981) Math. Program. , vol.20 , pp. 283-302
    • Frank, M.1
  • 95
    • 0042409109 scopus 로고
    • The equilibrium worth of a network link
    • Frank, M., The equilibrium worth of a network link. Transp. Sci. 23 (1989), 125–138.
    • (1989) Transp. Sci. , vol.23 , pp. 125-138
    • Frank, M.1
  • 96
    • 0001971618 scopus 로고
    • An algorithm for quadratic programming
    • Frank, M., Wolfe, P., An algorithm for quadratic programming. Nav. Res Logist. Q. 3 (1956), 95–110.
    • (1956) Nav. Res Logist. Q. , vol.3 , pp. 95-110
    • Frank, M.1    Wolfe, P.2
  • 97
    • 0015747007 scopus 로고
    • The flow-deviation method: an approach to store-and-forward computer communication network design
    • Fratta, L., Gerla, M., Kleinrock, L., The flow-deviation method: an approach to store-and-forward computer communication network design. Networks 3 (1973), 97–133.
    • (1973) Networks , vol.3 , pp. 97-133
    • Fratta, L.1    Gerla, M.2    Kleinrock, L.3
  • 98
    • 0022268736 scopus 로고
    • Transportation network equilibrium, design and aggregation: key developments and research opportunities
    • Friesz, T.L., Transportation network equilibrium, design and aggregation: key developments and research opportunities. Trans. Res. 19A (1985), 413–427.
    • (1985) Trans. Res. , vol.19A , pp. 413-427
    • Friesz, T.L.1
  • 99
    • 0021548770 scopus 로고
    • Alternative algorithms for the general network spatial price equilibrium problem
    • Friesz, T.L., Harker, P.T., Tobin, R.L., Alternative algorithms for the general network spatial price equilibrium problem. J. Region. Sci. 24 (1984), 475–507.
    • (1984) J. Region. Sci. , vol.24 , pp. 475-507
    • Friesz, T.L.1    Harker, P.T.2    Tobin, R.L.3
  • 100
    • 0021286348 scopus 로고
    • A modified Frank-Wolfe algorithm for solving the traffic assignment problem
    • Fukushima, M., A modified Frank-Wolfe algorithm for solving the traffic assignment problem. Trans. Res. 18B (1984), 169–177.
    • (1984) Trans. Res. , vol.18B , pp. 169-177
    • Fukushima, M.1
  • 101
    • 0021643928 scopus 로고
    • On the dual approach to the traffic assignment problem
    • Fukushima, M., On the dual approach to the traffic assignment problem. Trans. Res. 18B (1984), 235–245.
    • (1984) Trans. Res. , vol.18B , pp. 235-245
    • Fukushima, M.1
  • 102
    • 0022717559 scopus 로고
    • A relaxed projection method for variational inequalities
    • Fukushima, M., A relaxed projection method for variational inequalities. Math. Program. 35 (1986), 58–70.
    • (1986) Math. Program. , vol.35 , pp. 58-70
    • Fukushima, M.1
  • 103
    • 0026763569 scopus 로고
    • Equivalent differentiable optimization problems and descent methods for assymmetric variational inequalities
    • Fukushima, M., Equivalent differentiable optimization problems and descent methods for assymmetric variational inequalities. Math. Program. 53 (1992), 99–110.
    • (1992) Math. Program. , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 105
    • 0019011137 scopus 로고
    • Optimal traffic assignment with elastic demands: a review. Part I. Analysis framework
    • Gartner, N.H., Optimal traffic assignment with elastic demands: a review. Part I. Analysis framework. Transp. Sci. 14 (1980), 174–191.
    • (1980) Transp. Sci. , vol.14 , pp. 174-191
    • Gartner, N.H.1
  • 106
    • 0019011138 scopus 로고
    • Optimal traffic assignment with elastic demands: a review. Part II. Algorithmic approaches
    • Gartner, N.H., Optimal traffic assignment with elastic demands: a review. Part II. Algorithmic approaches. Transp. Sci. 14 (1980), 192–208.
    • (1980) Transp. Sci. , vol.14 , pp. 192-208
    • Gartner, N.H.1
  • 107
    • 0012358089 scopus 로고
    • A method for the traffic assignment problem when demand is elastic
    • Transportation Network Theory Unit, London Business School New York, NY
    • Gibert, A., A method for the traffic assignment problem when demand is elastic. Report LBS-TNT-85, 1968, Transportation Network Theory Unit, London Business School, New York, NY.
    • (1968) Report LBS-TNT-85
    • Gibert, A.1
  • 108
    • 0012358089 scopus 로고
    • A method for the traffic assignment problem
    • Transportation Network Theory Unit, London Business School London
    • Gibert, A., A method for the traffic assignment problem. Report LBS-TNT-95, 1968, Transportation Network Theory Unit, London Business School, London.
    • (1968) Report LBS-TNT-95
    • Gibert, A.1
  • 109
    • 0010758292 scopus 로고
    • Affine methods in nondifferentiable optimization
    • Center for Operations Research and Econometrics, Université Catholique de Louvain London
    • Goffin, J.L., Affine methods in nondifferentiable optimization. CORE Discussion paper No. 8744, 1987, Center for Operations Research and Econometrics, Université Catholique de Louvain, London, 24.
    • (1987) CORE Discussion paper No. 8744 , pp. 24
    • Goffin, J.L.1
  • 110
    • 0022717379 scopus 로고
    • Some comments on Wolfe's ‘away step’
    • Guélat, J., Marcotte, P., Some comments on Wolfe's ‘away step’. Math. Program. 35 (1986), 110–119.
    • (1986) Math. Program. , vol.35 , pp. 110-119
    • Guélat, J.1    Marcotte, P.2
  • 111
    • 0016947395 scopus 로고
    • Hydraulic network analysis using (generalized) geometric programming
    • Hall, M.A., Hydraulic network analysis using (generalized) geometric programming. Networks 6 (1976), 105–130.
    • (1976) Networks , vol.6 , pp. 105-130
    • Hall, M.A.1
  • 112
    • 0017998512 scopus 로고
    • Properties of the equilibrium state in transportation networks
    • Hall, M.A., Properties of the equilibrium state in transportation networks. Transp. Sci. 12 (1978), 208–216.
    • (1978) Transp. Sci. , vol.12 , pp. 208-216
    • Hall, M.A.1
  • 113
    • 0019006897 scopus 로고
    • SATURN — A simulation assignment model for the evaluation of traffic management schemes
    • Hall, M.A., Van Vliet, D., Willumsen, L.G., SATURN — A simulation assignment model for the evaluation of traffic management schemes. Traffic Eng. Control 21 (1980), 168–176.
    • (1980) Traffic Eng. Control , vol.21 , pp. 168-176
    • Hall, M.A.1    Van Vliet, D.2    Willumsen, L.G.3
  • 114
    • 38249041028 scopus 로고
    • A note on the existence of traffic equilibria
    • Harker, P.T., A note on the existence of traffic equilibria. Appl. Math. Comput. 18 (1986), 277–283.
    • (1986) Appl. Math. Comput. , vol.18 , pp. 277-283
    • Harker, P.T.1
  • 115
    • 0024013507 scopus 로고
    • Accelerating the convergence of the diagonalization and projection algorithms for finite-dimensional variational inequalities
    • Harker, P.T., Accelerating the convergence of the diagonalization and projection algorithms for finite-dimensional variational inequalities. Math. Program. 41 (1988), 29–59.
    • (1988) Math. Program. , vol.41 , pp. 29-59
    • Harker, P.T.1
  • 116
    • 0344704362 scopus 로고
    • Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications
    • Harker, P.T., Pang, J.-S., Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program. 48 (1990), 161–220.
    • (1990) Math. Program. , vol.48 , pp. 161-220
    • Harker, P.T.1    Pang, J.-S.2
  • 117
    • 85023470550 scopus 로고
    • Network aggregation in transportation planning models, Part I
    • Mathetech Louvain
    • Hearn, D.W., Network aggregation in transportation planning models, Part I. Report DOT-TSC-RSPD-78-8, 1978, Mathetech, Louvain.
    • (1978) Report DOT-TSC-RSPD-78-8
    • Hearn, D.W.1
  • 118
    • 85023436214 scopus 로고
    • Minimizing the gap function in certain convex programs
    • Report DOT-TSC-RSPA-79-18 Mathtec Princeton, NJ
    • Hearn, D.W., Minimizing the gap function in certain convex programs. Network Aggregation in Transportation Planning Models Report DOT-TSC-RSPA-79-18, 1979, Mathtec, Princeton, NJ, 60–82.
    • (1979) Network Aggregation in Transportation Planning Models , pp. 60-82
    • Hearn, D.W.1
  • 119
    • 0020116651 scopus 로고
    • The gap function of a convex program
    • Hearn, D.W., The gap function of a convex program. Oper. Res. Lett. 1 (1982), 67–71.
    • (1982) Oper. Res. Lett. , vol.1 , pp. 67-71
    • Hearn, D.W.1
  • 120
    • 23144461554 scopus 로고
    • Practical and theoretical aspects of aggregation problems in transportation planning models
    • M. Florian North-Holland Princeton, NJ
    • Hearn, D.W., Practical and theoretical aspects of aggregation problems in transportation planning models. Florian, M., (eds.) Transportation Planning Models, 1984, North-Holland, Princeton, NJ, 257–287.
    • (1984) Transportation Planning Models , pp. 257-287
    • Hearn, D.W.1
  • 121
    • 0001055816 scopus 로고
    • A dual ascent algorithm for traffic assignment problems
    • Hearn, D.W., Lawphongpanich, S., A dual ascent algorithm for traffic assignment problems. Trans. Res. 24B (1990), 423–430.
    • (1990) Trans. Res. , vol.24B , pp. 423-430
    • Hearn, D.W.1    Lawphongpanich, S.2
  • 122
    • 0021473876 scopus 로고
    • Convex programming formulations of the asymmetric traffic assignment problem
    • Hearn, D.W., Lawphongpanich, S., Nguyen, S., Convex programming formulations of the asymmetric traffic assignment problem. Trans. Res. 18B (1984), 357–365.
    • (1984) Trans. Res. , vol.18B , pp. 357-365
    • Hearn, D.W.1    Lawphongpanich, S.2    Nguyen, S.3
  • 124
    • 0023404413 scopus 로고
    • Restricted simplicial decomposition: computation and extensions
    • Hearn, D.W., Lawphongpanich, S., Ventura, J.A., Restricted simplicial decomposition: computation and extensions. Math. Program. Study 31 (1987), 99–118.
    • (1987) Math. Program. Study , vol.31 , pp. 99-118
    • Hearn, D.W.1    Lawphongpanich, S.2    Ventura, J.A.3
  • 126
    • 84910521496 scopus 로고
    • Dual and saddle functions related to the gap function
    • Department of Industrial and Systems Engineering, University of Florida Amsterdam
    • Hearn, D.W., Nguyen, S., Dual and saddle functions related to the gap function. Research Report 82-4, 1982, Department of Industrial and Systems Engineering, University of Florida, Amsterdam.
    • (1982) Research Report 82-4
    • Hearn, D.W.1    Nguyen, S.2
  • 128
    • 0019678850 scopus 로고
    • Convergence of the Frank-Wolfe method for certain bounded variable traffic assignment problems
    • Hearn, D.W., Ribera, J., Convergence of the Frank-Wolfe method for certain bounded variable traffic assignment problems. Trans. Res. 15B (1981), 437–442.
    • (1981) Trans. Res. , vol.15B , pp. 437-442
    • Hearn, D.W.1    Ribera, J.2
  • 129
    • 84976654365 scopus 로고
    • An efficient specialization of the convex simplex method for nonlinear network flow problems
    • Department of Industrial Engineering and Operations Research, Southern Methodist University Gainesville, FL
    • Helgason, R.V., Kennington, J.L., An efficient specialization of the convex simplex method for nonlinear network flow problems. Technical Report IEOR 77107, 1978, Department of Industrial Engineering and Operations Research, Southern Methodist University, Gainesville, FL.
    • (1978) Technical Report IEOR 77107
    • Helgason, R.V.1    Kennington, J.L.2
  • 130
    • 0016025237 scopus 로고
    • An extension of the Frank and Wolfe method of feasible directions
    • Holloway, C.A., An extension of the Frank and Wolfe method of feasible directions. Math. Program. 6 (1974), 14–27.
    • (1974) Math. Program. , vol.6 , pp. 14-27
    • Holloway, C.A.1
  • 131
    • 34147179608 scopus 로고
    • Models for traffic assignment
    • Jewell, W.S., Models for traffic assignment. Trans. Res. 1 (1967), 31–46.
    • (1967) Trans. Res. , vol.1 , pp. 31-46
    • Jewell, W.S.1
  • 132
    • 0019045340 scopus 로고
    • A maximum entropy combined distribution and assignment model solved by Benders decomposition
    • Jörnsten, K.O., A maximum entropy combined distribution and assignment model solved by Benders decomposition. Transp. Sci. 14 (1980), 262–276.
    • (1980) Transp. Sci. , vol.14 , pp. 262-276
    • Jörnsten, K.O.1
  • 133
    • 0004127781 scopus 로고
    • Algorithms for Network Programming
    • John Wiley & Sons Dallas, TX
    • Kennington, J.L., Helgason, R.V., Algorithms for Network Programming. 1980, John Wiley & Sons, Dallas, TX.
    • (1980)
    • Kennington, J.L.1    Helgason, R.V.2
  • 134
    • 0003467133 scopus 로고
    • An Introduction to Variational Inequalities and Their Applications
    • Academic Press New York, NY
    • Kinderlehrer, D., Stampacchia, G., An Introduction to Variational Inequalities and Their Applications. 1980, Academic Press, New York, NY.
    • (1980)
    • Kinderlehrer, D.1    Stampacchia, G.2
  • 135
    • 0003562232 scopus 로고
    • Communication Nets: Stochastic Message Flow and Delay
    • McGraw-Hill New York, NY
    • Kleinrock, L., Communication Nets: Stochastic Message Flow and Delay. 1964, McGraw-Hill, New York, NY.
    • (1964)
    • Kleinrock, L.1
  • 136
    • 0016319424 scopus 로고
    • An algorithm for nonlinear multicommodity flow problems
    • Klessig, R.W., An algorithm for nonlinear multicommodity flow problems. Networks 4 (1974), 343–355.
    • (1974) Networks , vol.4 , pp. 343-355
    • Klessig, R.W.1
  • 137
    • 0020822418 scopus 로고
    • A Newton method for convex separable network flow problems
    • Klincewicz, J.G., A Newton method for convex separable network flow problems. Networks 13 (1983), 427–442.
    • (1983) Networks , vol.13 , pp. 427-442
    • Klincewicz, J.G.1
  • 138
    • 84952259001 scopus 로고
    • Some fallacies in the interpretation of social costs
    • Knight, F.H., Some fallacies in the interpretation of social costs. Q. J. Econ. 38 (1924), 582–606.
    • (1924) Q. J. Econ. , vol.38 , pp. 582-606
    • Knight, F.H.1
  • 139
    • 0016570002 scopus 로고
    • Sandwich method for finding fixed points
    • Kuhn, H.W., MacKinnon, J.G., Sandwich method for finding fixed points. J. Optim. Theory Appl. 17 (1975), 189–204.
    • (1975) J. Optim. Theory Appl. , vol.17 , pp. 189-204
    • Kuhn, H.W.1    MacKinnon, J.G.2
  • 140
    • 0023401718 scopus 로고
    • Sensitivity analysis framework for variational inequalities
    • Kyparisis, J., Sensitivity analysis framework for variational inequalities. Math. Program. 38 (1987), 203–213.
    • (1987) Math. Program. , vol.38 , pp. 203-213
    • Kyparisis, J.1
  • 142
    • 0026822031 scopus 로고
    • Simplicial decomposition with disaggregated representation for the traffic assignment problem
    • Larsson, T., Patricksson, M., Simplicial decomposition with disaggregated representation for the traffic assignment problem. Trans. Sci. 26 (1992), 4–17.
    • (1992) Trans. Sci. , vol.26 , pp. 4-17
    • Larsson, T.1    Patricksson, M.2
  • 143
    • 0019058487 scopus 로고
    • Survey of nonlinear programming applications
    • Lasdon, L.S., Waren, A.D., Survey of nonlinear programming applications. Oper. Res. 28 (1980), 1029–1073.
    • (1980) Oper. Res. , vol.28 , pp. 1029-1073
    • Lasdon, L.S.1    Waren, A.D.2
  • 144
    • 0021286345 scopus 로고
    • Simplicial decomposition of the asymmetric traffic assignment problem
    • Lawphongpanich, S., Hearn, D.W., Simplicial decomposition of the asymmetric traffic assignment problem. Trans. Res. 18B (1984), 123–133.
    • (1984) Trans. Res. , vol.18B , pp. 123-133
    • Lawphongpanich, S.1    Hearn, D.W.2
  • 145
    • 0039596209 scopus 로고
    • Restricted simplicial decomposition with application to the traffic assignment problem
    • Lawphongpanich, S., Hearn, D.W., Restricted simplicial decomposition with application to the traffic assignment problem. Ric. Oper. 38 (1986), 97–120.
    • (1986) Ric. Oper. , vol.38 , pp. 97-120
    • Lawphongpanich, S.1    Hearn, D.W.2
  • 146
    • 0039703195 scopus 로고
    • Benders decomposition for variational inequalities
    • Lawphongpanich, S., Hearn, D.W., Benders decomposition for variational inequalities. Math. Program. 48 (1990), 231–247.
    • (1990) Math. Program. , vol.48 , pp. 231-247
    • Lawphongpanich, S.1    Hearn, D.W.2
  • 147
    • 0019636435 scopus 로고
    • Efficient algorithms for solving elastic demand traffic assignment problems and mode split-assignment problems
    • LeBlanc, L.J., Farhangian, K., Efficient algorithms for solving elastic demand traffic assignment problems and mode split-assignment problems. Transp. Sci. 15 (1981), 306–317.
    • (1981) Transp. Sci. , vol.15 , pp. 306-317
    • LeBlanc, L.J.1    Farhangian, K.2
  • 148
    • 0022151639 scopus 로고
    • Improved efficiency of the Frank-Wolfe algorithm for convex network programs
    • LeBlanc, L.J., Helgason, R.V., Boyce, D.E., Improved efficiency of the Frank-Wolfe algorithm for convex network programs. Transp. Sci. 19 (1985), 445–462.
    • (1985) Transp. Sci. , vol.19 , pp. 445-462
    • LeBlanc, L.J.1    Helgason, R.V.2    Boyce, D.E.3
  • 149
    • 0346784288 scopus 로고
    • An accurate and efficient approach to equilibrium traffic assignment on congested networks
    • TRB — National Academy of Sciences Linköping
    • LeBlanc, L.J., Morlok, E.K., Pierskalla, W.P., An accurate and efficient approach to equilibrium traffic assignment on congested networks. Trans. Res. Rec., 491, 1974, TRB — National Academy of Sciences, Linköping, 12–23.
    • (1974) Trans. Res. Rec. , vol.491 , pp. 12-23
    • LeBlanc, L.J.1    Morlok, E.K.2    Pierskalla, W.P.3
  • 150
    • 0016565756 scopus 로고
    • An efficient approach to solving the road network equilibrium traffic assignment problem
    • LeBlanc, L.J., Morlok, E.K., Pierskalla, W.P., An efficient approach to solving the road network equilibrium traffic assignment problem. Trans. Res. 9 (1975), 309–318.
    • (1975) Trans. Res. , vol.9 , pp. 309-318
    • LeBlanc, L.J.1    Morlok, E.K.2    Pierskalla, W.P.3
  • 151
    • 0015630518 scopus 로고
    • A column generation algorithm for optimal traffic assignment
    • Leventhal, T., Nemhauser, G., Trotter, L. Jr., A column generation algorithm for optimal traffic assignment. Transp. Sci. 7 (1973), 168–176.
    • (1973) Transp. Sci. , vol.7 , pp. 168-176
    • Leventhal, T.1    Nemhauser, G.2    Trotter, L.3
  • 152
    • 0022687650 scopus 로고
    • Convergence of the Frank-Wolfe algorithm in transportation networks
    • Lupi, M., Convergence of the Frank-Wolfe algorithm in transportation networks. Civ. Eng. Systems 3 (1986), 7–15.
    • (1986) Civ. Eng. Systems , vol.3 , pp. 7-15
    • Lupi, M.1
  • 153
    • 49549140671 scopus 로고
    • An algorithm for the generalized transportation problem
    • MacKinnon, J.G., An algorithm for the generalized transportation problem. Region. Sci. Urban Econ. 5 (1975), 445–464.
    • (1975) Region. Sci. Urban Econ. , vol.5 , pp. 445-464
    • MacKinnon, J.G.1
  • 154
    • 0040610728 scopus 로고
    • Models and algorithms for predicting urban traffic equilibria
    • M. Florian North-Holland Amsterdam
    • Magnanti, T.L., Models and algorithms for predicting urban traffic equilibria. Florian, M., (eds.) Transportation Planning Models, 1984, North-Holland, Amsterdam, 153–185.
    • (1984) Transportation Planning Models , pp. 153-185
    • Magnanti, T.L.1
  • 155
    • 84888692299 scopus 로고
    • Transportation planning: network models and their implementation
    • A.C. Hax
    • Magnanti, T.L., Golden, B.L., Transportation planning: network models and their implementation. Hax, A.C., (eds.) Studies in Operations Management, 1978, 465–518.
    • (1978) Studies in Operations Management , pp. 465-518
    • Magnanti, T.L.1    Golden, B.L.2
  • 156
    • 0347265435 scopus 로고
    • Some numerical results on the diagonalization algorithm for network assignment with asymmetric interactions between cars and trucks
    • Mahmassani, H.S., Mouskos, K.C., Some numerical results on the diagonalization algorithm for network assignment with asymmetric interactions between cars and trucks. Trans. Res. 22B (1988), 275–290.
    • (1988) Trans. Res. , vol.22B , pp. 275-290
    • Mahmassani, H.S.1    Mouskos, K.C.2
  • 157
    • 0022361866 scopus 로고
    • A new algorithm for solving variational inequalities with application to the traffic assignment problem
    • Marcotte, P., A new algorithm for solving variational inequalities with application to the traffic assignment problem. Math. Program. Study 33 (1985), 339–351.
    • (1985) Math. Program. Study , vol.33 , pp. 339-351
    • Marcotte, P.1
  • 159
    • 0023314787 scopus 로고
    • A note on a globally convergent Newton method for solving monotone variational inequalities
    • Marcotte, P., Dussault, J.-P., A note on a globally convergent Newton method for solving monotone variational inequalities. Oper. Res. Lett. 6 (1987), 35–42.
    • (1987) Oper. Res. Lett. , vol.6 , pp. 35-42
    • Marcotte, P.1    Dussault, J.-P.2
  • 160
    • 0024010208 scopus 로고
    • Adaptation of a modified Newton method for solving the asymmetric traffic equilibrium problem
    • Marcotte, P., Guélat, J., Adaptation of a modified Newton method for solving the asymmetric traffic equilibrium problem. Transp. Sci. 22 (1988), 112–124.
    • (1988) Transp. Sci. , vol.22 , pp. 112-124
    • Marcotte, P.1    Guélat, J.2
  • 161
    • 0026819758 scopus 로고
    • A Newton-SOR method for spatial price equilibrium
    • Marcotte, P., Marquis, G., Zubieta, L., A Newton-SOR method for spatial price equilibrium. Transp. Sci. 26 (1992), 36–47.
    • (1992) Transp. Sci. , vol.26 , pp. 36-47
    • Marcotte, P.1    Marquis, G.2    Zubieta, L.3
  • 162
    • 0000152718 scopus 로고
    • Generalized traffic equilibrium with probabilistic travel times and perceptions
    • Mirchandani, P., Soroush, H., Generalized traffic equilibrium with probabilistic travel times and perceptions. Transp. Sci. 21 (1987), 133–152.
    • (1987) Transp. Sci. , vol.21 , pp. 133-152
    • Mirchandani, P.1    Soroush, H.2
  • 163
    • 0011846869 scopus 로고
    • Road network traffic distribution in equilibrium
    • Matematisches Forschungsinstitut, Oberwolfach, October 1969, II. Oberwolfach-Tagung über Operations Research, Operations Research-Verfahren 8 R. Henn H.P. Künzi H. Schubert Anton Hain Verlag Amsterdam
    • Matematisches Forschungsinstitut, Oberwolfach, October 1969, II. Oberwolfach-Tagung über Operations Research, Operations Research-Verfahren 8 Murchland, J.D., Road network traffic distribution in equilibrium. Henn, R., Künzi, H.P., Schubert, H., (eds.) Proceedings of Mathematical Models in the Social Sciences, 1970, Anton Hain Verlag, Amsterdam, 145–183.
    • (1970) Proceedings of Mathematical Models in the Social Sciences , pp. 145-183
    • Murchland, J.D.1
  • 164
    • 0000490803 scopus 로고
    • Braess's paradox of traffic flow
    • Murchland, J.D., Braess's paradox of traffic flow. Transp. Res. 4 (1970), 391–394.
    • (1970) Transp. Res. , vol.4 , pp. 391-394
    • Murchland, J.D.1
  • 165
    • 0023104135 scopus 로고
    • Computational comparisons of spatial price equilibrium models
    • Nagurney, A., Computational comparisons of spatial price equilibrium models. J. Region. Sci. 27 (1987), 55–76.
    • (1987) J. Region. Sci. , vol.27 , pp. 55-76
    • Nagurney, A.1
  • 166
    • 84981454193 scopus 로고
    • Competitive equilibrium problems, variational inequalities and regional science
    • Nagurney, A., Competitive equilibrium problems, variational inequalities and regional science. J. Region. Sci. 27 (1987), 503–517.
    • (1987) J. Region. Sci. , vol.27 , pp. 503-517
    • Nagurney, A.1
  • 167
    • 45549113801 scopus 로고
    • An equilibration scheme for the traffic assignment problem with elastic demands
    • Nagurney, A., An equilibration scheme for the traffic assignment problem with elastic demands. Trans. Res. 22B (1988), 73–79.
    • (1988) Trans. Res. , vol.22B , pp. 73-79
    • Nagurney, A.1
  • 168
    • 84912921228 scopus 로고
    • An algorithm for the solution of a quadratic programming problem with application to constrained matrix and spatial price equilibrium problems
    • Nagurney, A., An algorithm for the solution of a quadratic programming problem with application to constrained matrix and spatial price equilibrium problems. Environ. Planning A 21 (1989), 99–114.
    • (1989) Environ. Planning A , vol.21 , pp. 99-114
    • Nagurney, A.1
  • 169
    • 0003762535 scopus 로고
    • Network Economics: A Variational Inequality Approach
    • Kluwer, Academic Publishers Meisenheim am Glan
    • Nagurney, A., Network Economics: A Variational Inequality Approach. 1993, Kluwer, Academic Publishers, Meisenheim am Glan.
    • (1993)
    • Nagurney, A.1
  • 170
    • 84964116707 scopus 로고
    • Parallel and serial variational inequality decomposition algorithms for multicommodity market equilibrium problems
    • Nagurney, A., Kim, D.-S., Parallel and serial variational inequality decomposition algorithms for multicommodity market equilibrium problems. Int. J. Supercomput. Appl. 3 (1989), 34–58.
    • (1989) Int. J. Supercomput. Appl. , vol.3 , pp. 34-58
    • Nagurney, A.1    Kim, D.-S.2
  • 172
    • 0042030427 scopus 로고
    • Affectations de trafic et tarification au coût marginal social: critique de quelques idées admises
    • Netter, M., Affectations de trafic et tarification au coût marginal social: critique de quelques idées admises. Trans. Res. 6 (1972), 411–429.
    • (1972) Trans. Res. , vol.6 , pp. 411-429
    • Netter, M.1
  • 173
    • 0012475615 scopus 로고
    • Traffic Flow on Transportation Networks
    • MIT Press New York, NY
    • Newell, G.F., Traffic Flow on Transportation Networks. 1980, MIT Press, New York, NY.
    • (1980)
    • Newell, G.F.1
  • 174
    • 0016092442 scopus 로고
    • An algorithm for the traffic assignment problem
    • Nguyen, S., An algorithm for the traffic assignment problem. Transp. Sci. 8 (1974), 203–216.
    • (1974) Transp. Sci. , vol.8 , pp. 203-216
    • Nguyen, S.1
  • 176
    • 0021427308 scopus 로고
    • An efficient method for computing traffic equilibria in networks with asymmetric transportation costs
    • Nguyen, S., Dupuis, C., An efficient method for computing traffic equilibria in networks with asymmetric transportation costs. Transp. Sci. 18 (1984), 185–202.
    • (1984) Transp. Sci. , vol.18 , pp. 185-202
    • Nguyen, S.1    Dupuis, C.2
  • 177
    • 84910395439 scopus 로고
    • TRAFFIC — an equilibrium traffic assignment program
    • Centre de Recherche sur les Transports, Université de Montréal Berlin
    • Nguyen, S., James, L., TRAFFIC — an equilibrium traffic assignment program. Publication #17, 1975, Centre de Recherche sur les Transports, Université de Montréal, Berlin.
    • (1975) Publication #17
    • Nguyen, S.1    James, L.2
  • 178
    • 84981379831 scopus 로고
    • Solution of the general multicommodity spatial equilibrium problem by variational and complementarity methods
    • Pang, J.-S., Solution of the general multicommodity spatial equilibrium problem by variational and complementarity methods. J. Region. Sci. 24 (1984), 403–414.
    • (1984) J. Region. Sci. , vol.24 , pp. 403-414
    • Pang, J.-S.1
  • 179
    • 0022013294 scopus 로고
    • Asymmetric variational inequality problems over product sets: applications and iterative methods
    • Pang, J.-S., Asymmetric variational inequality problems over product sets: applications and iterative methods. Math. Program. 31 (1985), 206–219.
    • (1985) Math. Program. , vol.31 , pp. 206-219
    • Pang, J.-S.1
  • 180
    • 0020243016 scopus 로고
    • Iterative methods for variational and complementarity problems
    • Pang, J.-S., Chan, D., Iterative methods for variational and complementarity problems. Math. Program. 24 (1982), 284–313.
    • (1982) Math. Program. , vol.24 , pp. 284-313
    • Pang, J.-S.1    Chan, D.2
  • 181
    • 0021488947 scopus 로고
    • Linearized simplicial decomposition methods for computing traffic equilibria on networks
    • Pang, J.-S., Yu, C.-S., Linearized simplicial decomposition methods for computing traffic equilibria on networks. Networks 14 (1984), 427–438.
    • (1984) Networks , vol.14 , pp. 427-438
    • Pang, J.-S.1    Yu, C.-S.2
  • 183
    • 0003586775 scopus 로고
    • The Traffic Assignment Problem — Models and Methods
    • VSP Linköping
    • Patricksson, M., The Traffic Assignment Problem — Models and Methods. 1994, VSP, Linköping.
    • (1994)
    • Patricksson, M.1
  • 184
    • 0016554251 scopus 로고
    • A primal-dual traffic assignment algorithm
    • Petersen, E.R., A primal-dual traffic assignment algorithm. Manage. Sci. 22 (1975), 87–95.
    • (1975) Manage. Sci. , vol.22 , pp. 87-95
    • Petersen, E.R.1
  • 185
    • 0010465579 scopus 로고
    • Flows in Transportation Networks
    • Academic Press Utrecht
    • Academic Potts, R.B., Oliver, R.M., Flows in Transportation Networks. 1972, Press, Utrecht.
    • (1972)
    • Potts, R.B.1    Oliver, R.M.2
  • 186
    • 0020091589 scopus 로고
    • The convergence of equilibrium algorithms with predetermined step sizes
    • Powell, W.B., Sheffi, Y., The convergence of equilibrium algorithms with predetermined step sizes. Transp. Sci. 16 (1982), 45–55.
    • (1982) Transp. Sci. , vol.16 , pp. 45-55
    • Powell, W.B.1    Sheffi, Y.2
  • 187
    • 0000352299 scopus 로고
    • Sensitivity analysis for variational inequalities defined on polyhedral sets
    • Qiu, Y., Magnanti, T.L., Sensitivity analysis for variational inequalities defined on polyhedral sets. Math. Oper. Res. 14 (1989), 410–432.
    • (1989) Math. Oper. Res. , vol.14 , pp. 410-432
    • Qiu, Y.1    Magnanti, T.L.2
  • 188
    • 0008717735 scopus 로고
    • Sensitivity analysis for variational inequalities
    • Qiu, Y., Magnanti, T.L., Sensitivity analysis for variational inequalities. Math. Oper. Res. 17 (1992), 61–76.
    • (1992) Math. Oper. Res. , vol.17 , pp. 61-76
    • Qiu, Y.1    Magnanti, T.L.2
  • 189
    • 84981594772 scopus 로고
    • The network equilibrium problem in integers
    • Rosenthal, R.W., The network equilibrium problem in integers. Networks 3 (1973), 53–59.
    • (1973) Networks , vol.3 , pp. 53-59
    • Rosenthal, R.W.1
  • 190
    • 85023494598 scopus 로고
    • The prediction of network equilibrium: the state of the art
    • Bruges
    • Bruges Ruiter, E.R., The prediction of network equilibrium: the state of the art. Proc. Int. Conf. on Transportation Research, 1973, 717–726.
    • (1973) Proc. Int. Conf. on Transportation Research , pp. 717-726
    • Ruiter, E.R.1
  • 191
    • 84910289460 scopus 로고
    • Implementation of operational network equilibrium procedures
    • Ruiter, E.R., Implementation of operational network equilibrium procedures. Trans. Res. Record 491 (1974), 40–51.
    • (1974) Trans. Res. Record , vol.491 , pp. 40-51
    • Ruiter, E.R.1
  • 192
    • 0000705122 scopus 로고
    • Spatial price equilibrium and linear programming
    • Samuelson, P.A., Spatial price equilibrium and linear programming. Am. Econ. Rev. 42 (1952), 283–303.
    • (1952) Am. Econ. Rev. , vol.42 , pp. 283-303
    • Samuelson, P.A.1
  • 193
    • 77957652183 scopus 로고
    • Convergence of decomposition algorithms for the traffic assignment problem
    • P. Hansen North-Holland Publishing Company New York, NY
    • Serra, P., Weintraub, A., Convergence of decomposition algorithms for the traffic assignment problem. Hansen, P., (eds.) Studies on Graphs and Discrete Programming, Annals of Discrete Mathematics, 1981, North-Holland Publishing Company, New York, NY, 313–318.
    • (1981) Studies on Graphs and Discrete Programming, Annals of Discrete Mathematics , pp. 313-318
    • Serra, P.1    Weintraub, A.2
  • 194
    • 0006148685 scopus 로고
    • Some algorithms for minimizing a function of several variables
    • Shah, B.V., Buehler, R.J., Kempthorne, O., Some algorithms for minimizing a function of several variables. SIAM J. Appl. Math. 12 (1964), 74–92.
    • (1964) SIAM J. Appl. Math. , vol.12 , pp. 74-92
    • Shah, B.V.1    Buehler, R.J.2    Kempthorne, O.3
  • 195
    • 0003582236 scopus 로고
    • Urban Transportation Networks. Equilibrium Analysis with Mathematical Programming Methods
    • Prentice-Hall Englewood Cliffs, NJ
    • Sheffi, Y., Urban Transportation Networks. Equilibrium Analysis with Mathematical Programming Methods. 1985, Prentice-Hall, Englewood Cliffs, NJ.
    • (1985)
    • Sheffi, Y.1
  • 196
    • 0019367092 scopus 로고
    • A comparison of stochastic and deterministic traffic assignment over congested networks
    • Sheffi, Y., Powell, W., A comparison of stochastic and deterministic traffic assignment over congested networks. Trans. Res. 15B (1981), 53–64.
    • (1981) Trans. Res. , vol.15B , pp. 53-64
    • Sheffi, Y.1    Powell, W.2
  • 197
    • 0020140779 scopus 로고
    • An algorithm for the equilibrium assignment problem with random link times
    • Sheffi, Y., Powell, W., An algorithm for the equilibrium assignment problem with random link times. Networks 12 (1982), 191–207.
    • (1982) Networks , vol.12 , pp. 191-207
    • Sheffi, Y.1    Powell, W.2
  • 198
    • 0018671988 scopus 로고
    • The marginal cost taxation of a transportation network
    • Smith, M.J., The marginal cost taxation of a transportation network. Trans. Res. 13B (1979), 237–242.
    • (1979) Trans. Res. , vol.13B , pp. 237-242
    • Smith, M.J.1
  • 199
    • 0018656183 scopus 로고
    • Existence, uniqueness and stability of traffic equilibria
    • Smith, M.J., Existence, uniqueness and stability of traffic equilibria. Trans. Res. 13B (1979), 295–304.
    • (1979) Trans. Res. , vol.13B , pp. 295-304
    • Smith, M.J.1
  • 200
    • 0020971858 scopus 로고
    • The existence and calculation of traffic equilibria
    • Smith, M.J., The existence and calculation of traffic equilibria. Trans. Res. 17B (1983), 291–303.
    • (1983) Trans. Res. , vol.17B , pp. 291-303
    • Smith, M.J.1
  • 201
    • 0020970488 scopus 로고
    • An algorithm for solving asymmetric equilibrium problems with a continuous cost-flow function
    • Smith, M.J., An algorithm for solving asymmetric equilibrium problems with a continuous cost-flow function. Trans. Res. 17B (1983), 365–371.
    • (1983) Trans. Res. , vol.17B , pp. 365-371
    • Smith, M.J.1
  • 202
    • 0021285924 scopus 로고
    • Two alternative definitions of traffic equilibrium
    • Smith, M.J., Two alternative definitions of traffic equilibrium. Trans. Res. 18B (1984), 63–65.
    • (1984) Trans. Res. , vol.18B , pp. 63-65
    • Smith, M.J.1
  • 203
    • 84910303495 scopus 로고
    • Planification d'une flotte d'avions
    • Centre for Research on Transportation, Université de Montréal Englewood Cliffs, NJ
    • Soumis, F., Planification d'une flotte d'avions. Publication #133, 1978, Centre for Research on Transportation, Université de Montréal, Englewood Cliffs, NJ.
    • (1978) Publication #133
    • Soumis, F.1
  • 204
    • 0004211617 scopus 로고
    • Optimization of Transport Networks
    • John Wiley & Sons London
    • Steenbrink, P.A., Optimization of Transport Networks. 1974, John Wiley & Sons, London.
    • (1974)
    • Steenbrink, P.A.1
  • 205
    • 0024106854 scopus 로고
    • The prevalence of paradoxes in transportation equilibrium problems
    • Steinberg, R., Stone, R.E., The prevalence of paradoxes in transportation equilibrium problems. Transp. Sci. 22 (1988), 231–241.
    • (1988) Transp. Sci. , vol.22 , pp. 231-241
    • Steinberg, R.1    Stone, R.E.2
  • 206
    • 0020804745 scopus 로고
    • The prevalence of Braess' paradox
    • Steinberg, R., Zangwill, W.I., The prevalence of Braess' paradox. Transp. Sci. 17 (1983), 301–318.
    • (1983) Transp. Sci. , vol.17 , pp. 301-318
    • Steinberg, R.1    Zangwill, W.I.2
  • 207
    • 0018911688 scopus 로고
    • Equilibrium vs. system-optimal flow: some examples
    • Stewart, N.F., Equilibrium vs. system-optimal flow: some examples. Trans. Res. 14A (1980), 81–84.
    • (1980) Trans. Res. , vol.14A , pp. 81-84
    • Stewart, N.F.1
  • 208
    • 0001681604 scopus 로고
    • Equilibrium among spatially separated markets: A reformulation
    • Takayama, T., Judge, G., Equilibrium among spatially separated markets: A reformulation. Econometrica 32 (1964), 510–524.
    • (1964) Econometrica , vol.32 , pp. 510-524
    • Takayama, T.1    Judge, G.2
  • 209
    • 0003932791 scopus 로고
    • Spatial and temporal price and allocation models
    • North-Holland London
    • Takayama, T., Judge, G., Spatial and temporal price and allocation models. 1971, North-Holland, London.
    • (1971)
    • Takayama, T.1    Judge, G.2
  • 211
    • 84910572778 scopus 로고
    • Calculation of fuel consumption due to traffic congestion in a case-study metropolitan area
    • Tobin, R.L., Calculation of fuel consumption due to traffic congestion in a case-study metropolitan area. Traffic Eng. Control 20 (1979), 101–113.
    • (1979) Traffic Eng. Control , vol.20 , pp. 101-113
    • Tobin, R.L.1
  • 212
    • 0023104225 scopus 로고
    • Sensitivity analysis for general spatial price equilibria
    • Tobin, R.L., Sensitivity analysis for general spatial price equilibria. J. Region. Sci. 27 (1987), 77–102.
    • (1987) J. Region. Sci. , vol.27 , pp. 77-102
    • Tobin, R.L.1
  • 213
    • 0024108601 scopus 로고
    • Sensitivity analysis for equilibrium network flow
    • Tobin, R.L., Friesz, T.L., Sensitivity analysis for equilibrium network flow. Transp. Sci. 22 (1988), 242–250.
    • (1988) Transp. Sci. , vol.22 , pp. 242-250
    • Tobin, R.L.1    Friesz, T.L.2
  • 214
    • 0016962669 scopus 로고
    • Road assignment — I. Principles and parameters of model formulation
    • Van Vliet, D., Road assignment — I. Principles and parameters of model formulation. Trans. Res. 10 (1976), 137–143.
    • (1976) Trans. Res. , vol.10 , pp. 137-143
    • Van Vliet, D.1
  • 215
    • 0016964333 scopus 로고
    • Road assignment — II. The GLTS model
    • Van Vliet, D., Road assignment — II. The GLTS model. Transp. Res. 10 (1976), 145–149.
    • (1976) Transp. Res. , vol.10 , pp. 145-149
    • Van Vliet, D.1
  • 216
    • 0016961734 scopus 로고
    • Road assignment — III. Comparative tests of stochastic methods
    • Van Vliet, D., Road assignment — III. Comparative tests of stochastic methods. Trans. Res. 10 (1976), 151–157.
    • (1976) Trans. Res. , vol.10 , pp. 151-157
    • Van Vliet, D.1
  • 217
    • 0023844758 scopus 로고
    • Computing the effective resistance in a system of conducting sticks
    • Ventura, J., Hearn, D.W., Computing the effective resistance in a system of conducting sticks. Comput. Ind. Eng. 14 (1988), 171–179.
    • (1988) Comput. Ind. Eng. , vol.14 , pp. 171-179
    • Ventura, J.1    Hearn, D.W.2
  • 218
    • 34250405253 scopus 로고
    • A finite algorithm to maximize certain pseudoconcave functions on polytopes
    • von Hohenbalken, B., A finite algorithm to maximize certain pseudoconcave functions on polytopes. Math. Program. 9 (1975), 189–206.
    • (1975) Math. Program. , vol.9 , pp. 189-206
    • von Hohenbalken, B.1
  • 219
    • 0002975378 scopus 로고
    • Simplicial decomposition in nonlinear programming algorithms
    • von Hohenbalken, B., Simplicial decomposition in nonlinear programming algorithms. Math. Program. 13 (1977), 49–68.
    • (1977) Math. Program. , vol.13 , pp. 49-68
    • von Hohenbalken, B.1
  • 220
    • 0003310913 scopus 로고
    • Some theoretical aspects of road traffic research
    • Part II Wardrop, J.G., Some theoretical aspects of road traffic research. Proc. Institute of Civil Engineers, 1952, 325–378.
    • (1952) Proc. Institute of Civil Engineers , pp. 325-378
    • Wardrop, J.G.1
  • 221
    • 0002902841 scopus 로고
    • A primal algorithm to solve network flow problems with convex costs
    • Weintraub, A., A primal algorithm to solve network flow problems with convex costs. Manage. Sci. 21 (1974), 87–97.
    • (1974) Manage. Sci. , vol.21 , pp. 87-97
    • Weintraub, A.1
  • 222
    • 84987028585 scopus 로고
    • An algorithm for the traffic assignment problem
    • Weintraub, A., Gonzáles, J., An algorithm for the traffic assignment problem. Networks 10 (1980), 197–209.
    • (1980) Networks , vol.10 , pp. 197-209
    • Weintraub, A.1    Gonzáles, J.2
  • 223
    • 0022268519 scopus 로고
    • Accelerating convergence of the Frank-Wolfe algorithm
    • Weintraub, A., Ortiz, C., González, J., Accelerating convergence of the Frank-Wolfe algorithm. Trans. Res. 19B (1985), 113–122.
    • (1985) Trans. Res. , vol.19B , pp. 113-122
    • Weintraub, A.1    Ortiz, C.2    González, J.3
  • 224
    • 0001945554 scopus 로고
    • Convergence theory in nonlinear programming
    • J. Abadie North-Holland Amsterdam
    • Wolfe, P., Convergence theory in nonlinear programming. Abadie, J., (eds.) Integer and Nonlinear Programming, 1970, North-Holland, Amsterdam, 1–36.
    • (1970) Integer and Nonlinear Programming , pp. 1-36
    • Wolfe, P.1
  • 225
    • 84918710926 scopus 로고
    • A general descent framework for the montone variational inequality problem
    • Centre de Recherche sur les Transports, Université de Montréal Amsterdam
    • Wu, J.H., Florian, M., Marcotte, P., A general descent framework for the montone variational inequality problem. Publication #723, 1990, Centre de Recherche sur les Transports, Université de Montréal, Amsterdam.
    • (1990) Publication #723
    • Wu, J.H.1    Florian, M.2    Marcotte, P.3
  • 226
    • 84878676338 scopus 로고
    • A new optimization formulation of the variational inequality problem with application to the network equilibrium problem
    • Centre de Recherche sur les Transports, Université de Montréal Montréal
    • Wu, J.H., Florian, M., Marcotte, P., A new optimization formulation of the variational inequality problem with application to the network equilibrium problem. Publication #722, 1991, Centre de Recherche sur les Transports, Université de Montréal, Montréal.
    • (1991) Publication #722
    • Wu, J.H.1    Florian, M.2    Marcotte, P.3
  • 227
    • 0002116806 scopus 로고
    • Two methods of search for equilibrium points of n-person concave games
    • Zuhovickiľ, S.I., Poljak, R.A., Primak, M.E., Two methods of search for equilibrium points of n-person concave games. Sov. Math. Dokl. 10 (1969), 279–282.
    • (1969) Sov. Math. Dokl. , vol.10 , pp. 279-282
    • Zuhovickiľ, S.I.1    Poljak, R.A.2    Primak, M.E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.