V. Aguilera, S. Allio, V. Benezech, F. Combes, and C. Millon, Estimating the quality of service of underground transit systems with cellular network data, Paper presented in the 4 th Transportation Research Arena Conference, 2012.

I. Andreasson, A method for the analysis of transit networks, Proceeding of the 2 nd European Congress on operations Research (Edited by Mark Roubens), 1976.

J. Añez, T. De-la-barra, and B. Pérez, Dual graph representation of transportation networks Simulating pedestrian movement in dynamic environments, Transportation Research Part B Cybergeo: European Journal of Geography, vol.305, issue.4, pp.209-216, 1996.

M. Beckmann, C. B. Mcguire, and C. B. Winsten, Studies In The Economics of Transportation, Transportation Research Part B, vol.29, issue.4, pp.287-295, 1955.

V. Benezech, experience of quality of service in urban transport networks : A Stochastic Approach -Est, 2013.

V. Benezech, F. Combes, and F. Leurent, Analysis of the variability of travel conditions along a transit line, Paper presented at TRB Annual Meeting, 2013.

V. J. Blue and J. L. Adler, Cellular automata microsimulation for modelling bi-directional pedestrian walkways, Transportation Research Part B, vol.3510, p.312, 2001.

J. R. Blum, B. Bouzaiene-ayari, M. Gendreau, and S. Nguyen, An equilibrium-fixed point model for passenger assignment in congested transit networks, Multidimensional Stochastic Approximation Methods Modelling Bus Stops in Transit Networks : A survey and New Formulations, pp.737-744, 1954.

L. T. Buckman and J. A. Leather, Modeling station congestion the PEDROUTE way Traffic Assignment Manual, 15] Cepeda M de transport en commun, pp.373-377, 1964.

M. Cepeda, R. Cominetti, and M. Florian, A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria, Transportation Research Part B: Methodological, vol.40, issue.6, pp.437-459, 2006.
DOI : 10.1016/j.trb.2005.05.006

I. Chabini, Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time, Master « Cité et Mobilité », References Modelling Congestion in Passenger Transit Networks [19] Chandakas E, pp.170-175, 1998.
DOI : 10.3141/1645-21

D. Réseau, Working Document, Ecole Nationale des Ponts et Chaussées, Note sur la Capacité du Matériel Roulant et son, 2008.

W. Affectation-sur-le-réseau-francilien, E. Document-chandakas, F. Leurent, F. Leurent, A. Poulhes et al., A Transit Station Model for Passenger Traffic Assignment with Capacity Constraints for a Transit Network, Paper #1993 presented in the 13 th WCTR Conference A Transit Assignment Model with Capacity Constraints: A Large-Scale Implementation, Paper #1440 presented in the 13 th WCTR Conference, Un modèle de trafic de voyageurs en transports collectifs, sensible aux contraintes de capacité, pp.167-188, 2013.

E. Chandakas, F. Leurent, and A. Poulhès, Les contraintes de capacité dans les trafics de voyageurs et de véhicules en transport collectif : un modèle de simulation et son application au Grand Paris, Paper presented at the ATEC ITS France Conference, 2014.

G. Cohen, Auxiliary problem principle extended to variational inequalities, Journal of Optimization Theory and Applications, vol.24, issue.3, 1988.
DOI : 10.1007/BF00938316

C. Chriqui and P. Robillard, Common Bus Lines, Transportation Science, vol.9, issue.2, pp.115-121, 1975.
DOI : 10.1287/trsc.9.2.115

R. Cominetti and J. Correa, Common-Lines and Passenger Assignment in Congested Transit Networks, Transportation Science, vol.35, issue.3, pp.250-267, 2001.
DOI : 10.1287/trsc.35.3.250.10154

W. Daamen, P. N. Daly, F. Mcgrath, and T. J. Annesley, SimPed : a Pedestrian Simulation Tool for Large Pedestrian Areas, conference proceedings EuroSIW Pedestrian speed/flow relationships for underground stations, Traffic Engineering and Control, vol.3231, issue.2, pp.24-26, 1991.

D. Cea, J. Fernandez, and E. , Transit Assignment to Minimal Routes: An efficient new Algorithm, Traffic Engineering and Control, vol.32, pp.491-494, 1989.

D. Cea, J. Fernandez, and E. , Transit Assignment for Congested Public Transport Systems: An equilibrium Model, Transportation Science, vol.2733, pp.133-147, 1993.

D. Cea, J. Bunster, J. P. Zubieta, L. Florian, and M. , Optimal Strategies and Optimal routes in public transit assignment models: an empirical comparison, Traffic Engineering and Control, vol.34, pp.520-526, 1988.

R. B. Dial and E. W. Dijkstra, Transit Pathfinder Algorithm, Highway Research Record 205, HRB, National Research Council A note on two problems in connexion with graphs, Valorisation de la régularité des radiales ferrées en Ile-de-Frane. Proceedings of the ATEC Congres, pp.67-85, 1959.

K. Fearnside and D. P. Drapper, Public Transport Assignment A new Approach, Traffic Engineering and Control, vol.13, pp.298-299, 1971.

J. Fiegel, A. Banos, and C. Bertelle, Modelling and Simulation of pedestrian behaviours in transport areas: the specific case of platform/train exchanges, Proceedings of ICCSA, An Algorithm for Quadratic Programming, pp.95-110, 1956.

G. Gallo, G. Longo, S. Pallottino, and S. Nguyen, Directed hypergraphs and applications, Discrete Applied Mathematics, vol.42, issue.2-3, pp.2-3, 1984.
DOI : 10.1016/0166-218X(93)90045-P

G. Gentille, S. Nguyen, and S. Pallottino, Route choice on transit networks with online information at stops, Transport Science, pp.289-297, 2005.

Z. Guo, N. H. Wilson, Y. Hamdouch, S. Lawphongpanich, Y. Hamdouch et al., Assessing the cost of transfer inconvenience in public transport systems: A case study of the London Underground Schedule-based transit assignment model with travel strategies and capacity constraints Schedule-based transit assignment model with vehicle capacity and seat availability, A Strategic Model for Dynamic Traffic Assignment, Networks and Spatial Economics, pp.91-104, 2004.

N. G. Harris, Capacity Restrained Simulation in Public Transport Environment, Traffic Engineering and Control, vol.3049, issue.6, 1989.

N. G. Harris, Modelling walk link congestion and the prioritisation of congestion relief, Traffic Engineering and Control, vol.3250, issue.2, pp.78-80, 1991.

N. G. Harris, Train boarding and alighting rates at high passenger loads, Journal of Advanced Transportation, vol.18, issue.1, pp.249-263, 2005.
DOI : 10.1002/atr.5670400302

N. G. Harris and R. J. Anderson, An international comparison of urban rail boarding and alighting rates, Public Transportation Planning A Mathematical Programming Approach, pp.521-526, 1989.
DOI : 10.1243/09544097JRRT115

D. Helbing and P. Molnar, Social force model for pedestrian dynamics, Physical Review E, vol.51, issue.5, pp.4282-4286, 1995.
DOI : 10.1103/PhysRevE.51.4282

S. P. Hoogendoorn, Normative Pedestrian Flow Behaviour: Theory and, 2001.

. Applications, Research Report Vk2001.02, Transportation and Traffic Engineering Section

S. P. Hoogendoorn and P. Bovy, Pedestrian route-choice and activity scheduling theory and models, Transportation Research Part B: Methodological, vol.38, issue.2, pp.169-190, 2004.
DOI : 10.1016/S0191-2615(03)00007-9

S. P. Hoogendoorn and W. Daamen, Pedestrian Behaviour at Bottlenecks, Transportation Science, vol.3958, issue.2, pp.147-159, 2005.
DOI : 10.1287/trsc.1040.0102

S. P. Hoogendoorn, M. Hauser, and N. Rodrigeus, Applying Microscopic Pedestrian Flow Simulation to Railway Station Design Evaluation in Lisbon, Portugal, Proceeedings of the 83rd Annual Meeting of Transportation Research Board Influence of the European Train Control System on the capacity of nodes, pp.83-94, 2004.
DOI : 10.3141/1878-11

H. Klüpfel, M. Schreckenberg, T. S. Meyer-könig, S. Luding, P. Bovy et al., Models for Crowd Movement and Egress Simulation, pp.357-372, 2005.

Y. Lai, S. Wang, and J. Jong, Development of analytical capacity models for commuter rail operations with advanced signaling systems, Paper #11- 3424 presented at the 90 th Annual Transportation Research Board Meeting, 2011.

W. H. Lam and M. G. Bell, Advanced Modelling for Transit Operations and Service Planning, pp.349-65, 2003.

W. H. Lam, C. Cheung, and C. F. Lam, A study of crowding effects at the, 1999.

W. H. Lam, Z. Y. Gao, K. S. Chan, and H. Yang, A stochastic user equilibrium assignment model for congested transit networks, Transportation Research Part B: Methodological, vol.33, issue.5, pp.351-368, 1999.
DOI : 10.1016/S0191-2615(98)00040-X

W. H. Lam, J. Zhou, and Z. Sheng, A capacity restraint transit assignment with elastic line frequency, Transept: A bus model, Traffic Engineering and Control, pp.68-82, 1976.
DOI : 10.1016/S0191-2615(01)00042-X

L. Clercq and F. , A public Transport Assignment Method, Traffic Engineering and Control, vol.1470, pp.91-96, 1972.

L. Figaro, Les franciliens souffrent de leurs transports en commun, Le Figaro report on 02les-franciliens-souffrent-de-leurs-transports-en-commun- .php> (accessed on, p.71, 2010.

L. Monde, La RATP achète 70 nouvelles rames pour renouveler celles du RER A, Le Monde report on, vol.72, 2012.

F. Leurent, On network assignment and supply-demand equilibrium: an analysis framework and a simple dynamic model, 2003.

F. Leurent, Confort et qualité de service en transport collectif urbain de voyageurs: analyse, modélisation et évaluation, Proceedings of the ATEC Congress, 2006.

F. Leurent and F. Leurent, modèle PSAT, multiclasse 0a, Working Document, Ecole Nationale des Ponts et Chaussées, 2010.

F. Leurent, Transport capacity constraints on the mass transit system: a systemic analysis, European Transport Research Review, vol.1878, issue.1, pp.2011-78, 2011.
DOI : 10.1007/s12544-011-0046-5

URL : https://hal.archives-ouvertes.fr/hal-00835219

F. Leurent, The Transit Bottleneck Model, Working Document, Ecole Nationale des Ponts et Chaussées, 2011.

F. Leurent, On seat capacity in traffic assignment to a transit network, Journal of Advanced Transportation, vol.28, issue.2, pp.112-138, 2012.
DOI : 10.1002/atr.146

URL : https://hal.archives-ouvertes.fr/hal-00652377

F. Leurent, A regularization process to yield smooth upper layer link flows with respect to link costs and frequencies in the CapTA model, 2012.

F. Leurent and Y. Askoura, The person capacity of a transit route: a review, assessment and benchmark of static models for network traffic assignment, Paper Presented at TRB Meeting, 2010.

F. Leurent and V. Benezech, The Passenger Stock and Attractivity Threshold Model for Traffic Assignment on a Public Transit Network with Capacity Constraint, Paper Presented at TRB Annual Meeting, 2011.

F. Leurent and E. Chandakas, Capacité des véhicules, attente à quai et modélisation pour la planification du réseau TC, Modélisation Urbaine : de la Représentation au Projet. Collection Références du Commissariat Général au développement durable, pp.192-195, 2012.

F. Leurent and E. Chandakas, The Transit Bottleneck Model, Procedia - Social and Behavioral Sciences, vol.54, pp.822-833, 2012.
DOI : 10.1016/j.sbspro.2012.09.798

URL : https://hal.archives-ouvertes.fr/hal-00852523

F. Leurent and K. Liu, On seat congestion, passenger comfort and route choice in urban transit: a network equilibrium assignment model with application to Paris, Paper Presented at TRB Annual Meeting, 2009.

F. Leurent, E. Chandakas, and A. Poulhes, User and service equilibrium in a structural model of traffic assignment to a transit network, The State of the Art in the European Quantitative Oriented Transportation and Logistics Research 14th Euro Working Group on Transportation & 26th Mini Euro, 2011.
DOI : 10.1016/j.sbspro.2011.08.056

URL : https://hal.archives-ouvertes.fr/hal-00852962

F. Leurent, E. Chandakas, and A. Poulhes, A Passenger Traffic Assignment Model with Capacity Constraints for Transit Networks, Procedia - Social and Behavioral Sciences, vol.54, pp.772-784, 2012.
DOI : 10.1016/j.sbspro.2012.09.794

URL : https://hal.archives-ouvertes.fr/hal-00852526

F. Leurent, E. Chandakas, and A. Poulhes, Bi-layer equilibrium of user and service in a capacitated model of traffic assignment to a transit network. Working paper submitted for publication to European Transport, 2012.

T. Lin and N. H. Wilson, Dwell Time Relationships for Light Rail Systems, Transportation Research Record, vol.136190, pp.287-295, 1992.

P. Marcotte and S. Nguyen, Hyperpath Formulations of Traffic Assignment Problems, 1998.
DOI : 10.1007/978-1-4615-5757-9_9

P. Marcotte, S. Nguyen, and A. Schoeb, A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks, Operations Research, vol.52, issue.2, pp.191-212, 2004.
DOI : 10.1287/opre.1030.0091

P. Merlin, Géographie, économie et planification des transports, pp.480-95, 1991.

L. Meschini, G. Gentile, and N. Papola, A frequency-based transit model for dynamic traffic assignment to multimodal networks, Presented at 17 th International Symposium on Transportation and Traffic Theory, 2007.

P. Milgrom and I. Segal, Envelope Theorems for Arbitrary Choice Sets Assignment model of timetable based systems, Proceedings of 27 th European Transportation Forum NFPA 130: Standard for Fixed Guideway Transit and Passenger Rail Systems, pp.583-601, 1999.

S. Nguyen and S. Pallottino, Equilibrium traffic assignment for large scale transit networks, European Journal of Operational Research, vol.37, issue.2, pp.176-186, 1988.
DOI : 10.1016/0377-2217(88)90327-X

S. Nguyen, S. Pallottino, and F. Malucelli, A modelling Framework for Passenger Assignment on a Transport Network with Timetables, Transportation Science, vol.35, issue.238, p.249, 2001.

A. Nuzzolo, U. Crisalli, and L. Rosati, A schedule-based assignment model with explicit capacity constraints for congested transit networks, Proceeding of European Transport Conference, 2007.
DOI : 10.1016/j.trc.2011.02.007

A. Nuzzolo, U. Crisalli, and L. Rosati, A schedule-based assignment model with explicit capacity constraints for congested transit networks, Transportation Research Part C: Emerging Technologies, vol.20, issue.1, pp.16-33, 2012.
DOI : 10.1016/j.trc.2011.02.007

A. Nuzzolo, F. Russo, and U. Crisalli, A Doubly Dynamic Schedule-based Assignment Model for Transit Networks, Transportation Science, vol.35, issue.3, p.285, 2001.
DOI : 10.1287/trsc.35.3.268.10149

. Oxford-economic and . Forecasting, The Economic Effects of Transport Delays on the City of London, 2003.

S. Paris, S. Donikian, and N. Bonvalet, Environmental abstraction and path planning techniques for realistic crowd simulation, Computer Animation and Virtual Worlds, vol.407, issue.3-4, pp.325-335, 2006.
DOI : 10.1002/cav.136

A. Poulhes and E. Chandakas, Simulateur de Flux de Voyageurs dans les Transports Collectifs Urbains, 2011.

B. Pushkarev and J. Zupan, Urban Space for Pedestrians, 1975.

P. Robillard, (0,1) Hyperbolic Programming Problem, Naval Research Log Quart, vol.18, p.1, 1971.

J. Schmöcker, M. G. Bell, and F. Kurauchi, A quasi-dynamic capacity constrained frequency-based transit assignment model, Transportation Research Part B: Methodological, vol.42, issue.10, p.945, 2008.
DOI : 10.1016/j.trb.2008.02.001

J. Schmöcker, A. Fonzone, M. G. Bell, F. Kurauchi, and H. Shimamoto, Frequency-based transit assignment considering seat capacities, Transportation Research Part B: Methodological, vol.45, issue.2, p.408, 2011.
DOI : 10.1016/j.trb.2010.07.002

H. Shimamoto, F. Kurauchi, Y. Iida, J. Schmocker, and M. G. Bell, Evaluation of public transport congestion mitigation measures using a passenger assignment model, Journal of the Eastern Asia Transportation Studies, vol.6, pp.2076-2091, 2005.

H. Spiess, On Optimum Route Choice Strategies in Transit Networks, Pub, vol.286, 1983.

H. Spiess and M. Florian, Optimal strategies: A new assignment model for transit networks, Transportation Research Part B: Methodological, vol.23, issue.2, pp.83-121, 1989.
DOI : 10.1016/0191-2615(89)90034-9

A. Sumalee, T. Zhijia, and W. H. Lam, Dynamic stochastic transit assignment with explicit seat allocation model, Transportation Research Part B: Methodological, vol.43, issue.8-9, p.912, 2009.
DOI : 10.1016/j.trb.2009.02.009

T. Sumi, Y. Matsumoto, and Y. Miyaki, Departure time and route choice of commuters on mass transit systems, Transportation Research Part B: Methodological, vol.24, issue.4, pp.247-262, 1990.
DOI : 10.1016/0191-2615(90)90001-F

F. Teklu, A Stochastic Process Approach for Frequency-based Transit Assignment with Strict Capacity Constraints, Networks and Spatial Economics, vol.28, issue.2-3, p.240, 2007.
DOI : 10.1007/s11067-007-9046-3

K. Teknomo, Application of microscopic pedestrian simulation model, Transportation Research Part F: Traffic Psychology and Behaviour, vol.9, issue.1, p.27, 2006.
DOI : 10.1016/j.trf.2005.08.006

Q. Tian, H. Huang, and H. Yang, Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system, Transportation Research Part B: Methodological, vol.41, issue.6, pp.616-631, 2007.
DOI : 10.1016/j.trb.2006.10.003

C. O. Tong and S. C. Wong, A stochastic transit assignment model using a dynamic schedule-based network, Transportation Research Part B: Methodological, vol.33, issue.2, p.107, 1999.
DOI : 10.1016/S0191-2615(98)00030-7

C. O. Tong, S. C. Wong, M. H. Poon, and M. C. Tan, A schedule-based dynamic transit network model - Recent advances and prospective future research, Journal of Advanced Transportation, vol.26, issue.3, p.195, 2001.
DOI : 10.1002/atr.5670350207

V. Trozzi, I. Kaparias, M. G. Bell, and G. Gentile, A dynamic route choice model for public transport networks with boarding queues, Transportation Planning and Technology, vol.40, issue.6, pp.44-61, 2012.
DOI : 10.1287/trsc.28.3.193

V. Trozzi, G. Gentile, M. G. Bell, and I. Kaparias, Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths, Transportation Research Part B: Methodological, vol.57, pp.266-285, 2013.
DOI : 10.1016/j.trb.2013.06.011

V. R. Vuchic, Urban Transit: Operations, Planning and Economics, 2005.

J. G. Wardrop, CORRESPONDENCE. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH., Proceedings of the Institute of Civil Engineers, Part II, pp.325-378, 1952.
DOI : 10.1680/ipeds.1952.11362

S. C. Wong and C. O. Tong, Estimation of time-dependent origin???destination matrices for transit networks, Transportation Research Part B: Methodological, vol.32, issue.1, p.48, 1998.
DOI : 10.1016/S0191-2615(97)00011-8

J. H. Wu, M. Florian, and P. Marcotte, Transit Equilibrium Assignment: A Model and Solution Algorithms, Transportation Science, vol.28, issue.3, pp.193-203, 1994.
DOI : 10.1287/trsc.28.3.193