Solving network equilibrium problems on multimodal urban transportation networks with multiple user classes

References

• Aashtiani HZ (1979) The multimodal traffic assignment problem PhD dissertation, Alfred P. Sloan School of Management, MIT Cambridge MA
   Google Scholar
• Aashtiani , HZ and Magnanti , TL . (1981) . Equilibria on a congested transportation network . SIAM Journal of Algebraic and Discrete Methods , 2 : pp. 213–226
   Google Scholar
• Abdulaal , M and Leblanc , LJ . (1979) . Methods for combining modal split and equilibrium assignment models . Transportation Science , 13 : pp. 292–214
   Google Scholar
• Abkowitz , MD . (1981) . An analysis of the commuter departure time decision . Transportation , 10 : pp. 283–297
   Web of Science ®Google Scholar
• Abrahamsson , T and Lundqvist , L . (1999) . Formulation and estimation of combined network equilibrium models with applications to Stockholm . Transportation Science , 33 : pp. 80–100
   Web of Science ®Google Scholar
• Asmuth RL (1978) Traffic Network Equilibria Technical Report SOL 78‐2 Stanford CA Systems Optimization Laboratory, Stanford University
   Google Scholar
• Beckmann MJ McGuire CB Winsten CB (1956) Studies in the Economics of Transportation New Haven CT Yale University Press
   Google Scholar
• Bhat , CR . (1998) . Analysis of travel mode and departure time choice for urban shopping trips . Transportation Research , 6B : pp. 361–371
   Google Scholar
• Bianchi , R , Jara‐Diaz , SR and Ortuzar , Jde D . (1998) . Modelling new pricing strategies for the Santiago Metro . Transport Policy , 5 : pp. 223–232
   Google Scholar
• Boyce , D . (2002) . Is the sequential travel forecasting paradigm counterproductive? . ASCE Journal of Urban Planning and Development , 128 : pp. 169–183
   Web of Science ®Google Scholar
• Boyce , D and Bar‐Gera , H . (2003) . Validation of multiclass urban travel forecasting models combining origin–destination, mode and route choices . Journal of Regional Science , 43 : pp. 517–540
   Web of Science ®Google Scholar
• Boyce , D and Bar‐Gera , H . (2004) . Multiclass combined models for urban travel forecasting . Network and Spatial Economics , 4 : pp. 115–124
   Web of Science ®Google Scholar
• Boyce , D , Lupa , MR and Zhang , Y . (1994) . Introducing ‘feedback’ into four‐step travel forecasting procedure versus equilibrium solution of combined model . Transportation Research Record , 1443 : pp. 65–74
   Google Scholar
• Bruynooghe M (1969) Un modèle integré de distribution, de traffic sur un réseau Technical Report (Arcueil: Departement de Recherche Operationnelle et Infoematique)
   Google Scholar
• Chin , ATH . (1990) . Influences on commuter trip departure time decisions in Singapore . Transportation Research , 24A : pp. 321–333
   Google Scholar
• Chriqui , C and Robillard , P . (1975) . Common bus lanes . Transportation Science , 9 : pp. 115–121
   Google Scholar
• Dafermos , S . (1971) . An extended traffic assignment model with applications to two‐way traffic . Transportation Science , 5 : pp. 366–389
   Google Scholar
• Dafermos , S . (1972) . The assignment problem for multiclass‐user transportation networks . Transportation Science , 6 : pp. 73–87
   Google Scholar
• Dafermos , S . (1980) . Traffic equilibrium and variational inequalities . Transportation Science , 14 : pp. 42–54
   Web of Science ®Google Scholar
• Dafermos , S . (1982a) . The general multimodal network equilibrium problem with elastic demand . Networks , 12 : pp. 57–72
   Web of Science ®Google Scholar
• Dafermos , S . (1982b) . Relaxation algorithms for the general asymmetric traffic equilibrium problem . Transportation Science , 16 : pp. 231–240
   Web of Science ®Google Scholar
• De Cea , J and Fernández , JE . (1993) . Transit assignment for congested public transport systems: an equilibrium model . Transportation Science , 27 : pp. 133–147
   Web of Science ®Google Scholar
• De Cea J Fernández JE (2000) Transit assignment models in: D. A. Hensher and K. J. Button (Eds) Handbook of Transport Modelling pp. 497–508 Amsterdam Elsevier
   Google Scholar
• De Cea J Fernández JE De Grange L (2004b) Combined models with hierarchical demand functions: a multi‐objective optimization approach Working Paper 88 Department of Transport Engineering, Pontificia Universidad Católica de Chile
   Google Scholar
• De Cea J Fernández JE Dekock V Soto A (2004a) Solving supply–demand equilibrium problems on multimodal urban transportation networks with multiple user classes Working Paper 87 Department of Transport Engineering, Pontificia Universidad Católica de Chile
   Google Scholar
• Dekock V (2001) Modelo de equilibrio simultáneo con elección de destino, modo y horario de viaje: formulación matemática y algoritmo de solución MSc thesis Department of Transport Engineering, Pontificia Universidad Católica de Chile
   Google Scholar
• Dekock V De Cea J Fernández JE (2002) Equilibrio simultáneo de distribución, partición modal y asignación con elección horaria de viajes in Proceedings CIT 2002 Santander Spain
   Google Scholar
• Evans , S . (1976) . Derivation and analysis of some models for combining distribution and assignment . Transportation Research , 10 : pp. 37–57
   Google Scholar
• Fernández JE De Cea J (1990) An application of equilibrium modelling to urban transport planning in developing countries: the case of Santiago de Chile in: H. E. Bradley (Ed.) Operational Research 90 pp. 367–378 Oxford Pergamon
   Google Scholar
• Fernández , JE and Friesz , TL . (1983) . Equilibrium predictions in transportation markets: the state of the art . Transportation Research , 17B : pp. 155–172
   Google Scholar
• Fernández , JE , De Cea , J and Soto , A . (2003) . A multimodal supply–demand equilibrium model for predicting intercity freight flows . Transportation Research , 37B : pp. 615–640
   Google Scholar
• Fernández , JE , De Cea , J , Florian , M and Cabrera , E . (1994) . Network equilibrium models with combined modes . Transportation Science , 28 : pp. 182–192
   Web of Science ®Google Scholar
• Fisk , C and Nguyen , S . (1982) . Solution algorithms for network equilibrium with asymmetric user costs . Transportation Science , 16 : pp. 361–381
   Web of Science ®Google Scholar
• Florian , M . (1977) . A traffic equilibrium model of travel by car and public transit modes . Transportation Science , 11 : pp. 166–179
   Google Scholar
• Florian M (1979) Asymmetrical Variable Demand Multi‐Mode Traffic Equilibrium Problems: Existence and Uniqueness of Solutions and a Solution Algorithm Divicao de Intercambio de Edicoes, INDO/0/0 Rio de Janeiro Pontificia Universidad Catolica
   Google Scholar
• Florian , M and Nguyen , S . (1978) . A combined trip distribution modal split and assignment model . Transportation Research , 12 : pp. 241–246
   Google Scholar
• Florian , M and Spiess , H . (1982) . The convergence of diagonalization algorithms for asymmetric network equilibrium problems . Transportation Research , 16B : pp. 447–483
   Google Scholar
• Florian , M , Nguyen , S and Ferland , J . (1975) . On the combined distribution assignment of traffic . Transportation Science , 9 : pp. 43–53
   Google Scholar
• Florian M Wu JH He S (1999) A multi‐class multi‐mode variable demand network equilibrium model with hierarchical logit structures in Actas IX Congreso Chileno de Ingeniería de Transporte Santiago Chile
   Google Scholar
• Frank , M and Wolfe , P . (1956) . An algorithm for quadratic programming . Naval Research Logistics Quarterly , 3 : pp. 95–110
   Google Scholar
• Harker PT Pang JS (1987) Finite‐dimensional Variational Inequality Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications Report 87‐12‐06 Philadelphia PA Warton School, University of Pennsylvania
   Google Scholar
• Hendrickson , C and Plank , E . (1984) . The flexibility of departure times for work trips . Transportation Research , 18A : pp. 25–36
   Google Scholar
• Johnston RH Bates JJ Roberts M (1989) A survey of peak spreading in London: methodology and initial results in: Proceedings of the 17th PTRC Annual Meeting University of Sussex Falmer UK
   Google Scholar
• Kullback S (1959) Information Theory and Statistics New York Wiley
   Google Scholar
• Le Clerq , F . (1972) . A public transport assignment method . Traffic Engineering and Control , 13 : pp. 91–96
   Google Scholar
• Manheim M (1979) Fundamentals of Transportation System Analysis Cambridge MA MIT Press
   Google Scholar
• McCafferty , D and Hall , FL . (1982) . The use of multinomial logit analysis to model the choice of time to travel . Economic Geography , 58 : pp. 236–246
   Web of Science ®Google Scholar
• Nguyen , S and Dupuis , C . (1984) . An efficient method for computing traffic equilibria in networks with asymmetric transportation costs . Transportation Science , 18 : pp. 185–202
   Web of Science ®Google Scholar
• Nguyen , S and Pallottino , S . (1988) . Equilibrium traffic assignment for large scale transit networks . European Journal of Operation Research , 5 : pp. 396–404
   Google Scholar
• Pang , JS and Chang , D . (1982) . Iterative methods for variational and complementarity problems . Mathematical Programming , 24 : pp. 284–313
   Web of Science ®Google Scholar
• Sheffi Y (1985) Urban Transportation Networks Englewood Cliffs NJ Prentice‐Hall
   Google Scholar
• Smith , MJ . (1979) . The existence, uniqueness and stability of traffic equilibria . Transportation Research , 13B : pp. 295–304
   Google Scholar
• Spiess , H and Florian , M . (1989) . Optimal strategies: a new assignment model for transit networks . Transportation Research , 23B : pp. 83–102
   Google Scholar
• Williams , HCWL . (1977) . On the formation of travel demand models and economic evaluation measures of user benefit . Environment and Planning , 9A : pp. 285–344
   Google Scholar
• Wu , JH , Florian , M and Marcotte , P . (1994) . Transit equilibrium assignment: a model and solution algorithms . Transportation Science , 28 : pp. 193–203
   Web of Science ®Google Scholar