Free Access
Volume 45, Number 1, January-February 2011
Page(s) 145 - 168
Published online 24 June 2010
  1. N. Bellomo and C. Dogbe, On the modelling crowd dynamics from scalling to hyperbolic macroscopic models. Math. Mod. Meth. Appl. Sci. 18 (2008) 1317–1345. [CrossRef]
  2. F. Bernicot and J. Venel, Existence of sweeping process in Banach spaces under directional prox-regularity. J. Convex Anal. 17 (2010) 451–484. [MathSciNet]
  3. V. Blue and J.L. Adler, Cellular automata microsimulation for modeling bi-directional pedestrian walkways. Transp. Res. B 35 (2001) 293–312. [CrossRef]
  4. A. Borgers and H. Timmermans, City centre entry points, store location patterns and pedestrian route choice behaviour: A microlevel simulation model. Socio-Econ. Plann. Sci. 20 (1986) 25–31. [CrossRef]
  5. A. Borgers and H. Timmermans, A model of pedestrian route choice and demand for retail facilities within inner-cityshopping areas. Geogr. Anal. 18 (1986) 115–128. [CrossRef]
  6. M. Bounkhel and L. Thibault, On various notions of regularity of sets in nonsmooth analysis. Nonlinear Convex Anal. 48 (2002) 223–246. [CrossRef]
  7. H. Brezis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. AM, North Holland (1973).
  8. C. Burstedde, K. Klauck, A. Schadschneider and J. Zittartz, Simulation of pedestrian dynamics using a two-dimensional cellular automaton. Physica A 295 (2001) 507–525. [CrossRef]
  9. G. Buttazzo, C. Jimenez and E. Oudet, An optimization problem for mass transportation with congested dynamics. SIAM J. Control Optim. 48 (2009) 1961–1976. [CrossRef] [MathSciNet]
  10. P.G. Ciarlet, Introduction à l'analyse numérique matricielle et à l'optimisation. Masson, Paris (1990).
  11. F.H. Clarke, R.J. Stern and P.R. Wolenski, Proximal smoothness and the lower-c2 property. J. Convex Anal. 2 (1995) 117–144. [MathSciNet]
  12. F.H. Clarke, Y.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York, Inc. (1998).
  13. W. Daamen, Modelling passenger flows in public transport facilities. Ph.D. Thesis, Technische Universiteit Delft, The Netherlands (2004).
  14. J.A. Delgado, Blaschke's theorem for convex hypersurfaces. J. Diff. Geom. 14 (1979) 489–496.
  15. C. Dogbé, On the numerical solutions of second order macroscopic models of pedestrian flows. Comput. Math. Appl. 56 (2008) 1884–1898. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  16. J.F. Edmond and L. Thibault, Relaxation of an optimal control problem involving a perturbed sweeping process. Math. Program., Ser. B 104 (2005) 347–373.
  17. J.F. Edmond and L. Thibault, BV solutions of nonconvex sweeping process differential inclusion with perturbation. J. Diff. Equ. 226 (2006) 135–179. [CrossRef]
  18. J.J. Fruin, Design for pedestrians: A level-of-service concept. Highway Research Record 355 (1971) 1–15.
  19. S. Gwynne, E.R. Galea, P.J. Lawrence and L. Filippidis, Modelling occupant interaction with fire conditions using the buildingEXODUS evacuation model. Fire Saf. J. 36 (2001) 327–357. [CrossRef]
  20. D. Helbing, A fluid-dynamic model for the movement of pedestrians. Complex Syst. 6 (1992) 391–415.
  21. D. Helbing and P. Molnár, Social force model for pedestrians dynamics. Phys. Rev. E 51 (1995) 4282–4286. [CrossRef]
  22. D. Helbing, I.J. Farkas and T. Vicsek, Simulating dynamical features of escape panic. Nature 407 (2000) 487. [CrossRef] [PubMed]
  23. L.F. Henderson, The stastitics of crowd fluids. Nature 229 (1971) 381–383. [CrossRef] [PubMed]
  24. S.P. Hoogendoorn and P.H.L. Bovy, Gas-kinetic modeling and simulation of pedestrian flows. Transp. Res. Rec. 1710 (2000) 28–36. [CrossRef]
  25. S.P. Hoogendoorn and P.H.L. Bovy, Pedestrian route-choice and activity scheduling theory and models. Transp. Res. B 38 (2004) 169–190. [CrossRef]
  26. S.P. Hoogendoorn and P.H.L. Bovy, Dynamic user-optimal assignment in continuous time and space. Transp. Res. B 38 (2004) 571–592. [CrossRef]
  27. R. Hughes, The flow of large crowds of pedestrians. Math. Comput. Simul. 53 (2000) 367–370. [CrossRef]
  28. R. Hughes, A continuum theory for the flow of pedestrians. Transp. Res. B 36 (2002) 507–535. [CrossRef]
  29. R. Kimmel and J. Sethian, Fast marching methods for computing distance maps and shortest paths. Technical Report 669, CPAM, Univ. of California, Berkeley (1996).
  30. A. Kirchner and A. Schadschneider, Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrians dynamics. Physica A 312 (2002) 260–276. [CrossRef]
  31. H. Klüpfel and T. Meyer-König, Characteristics of the pedgo software for crowd movement and egress simulation, in Pedestrian and Evacuation Dynamics 2003, E. Galea Ed., University of Greenwich, CMS Press, London (2003) 331–340.
  32. A. Lefebvre, Modélisation numérique d'écoulements fluide/particules, Prise en compte des forces de lubrification. Ph.D. Thesis, Université Paris-Sud XI, Faculté des sciences d'Orsay, France (2007).
  33. A. Lefebvre, Numerical simulations of gluey particles. ESAIM: M2AN 43 (2009) 53–80. [CrossRef] [EDP Sciences]
  34. G.G. Løvås, Modelling and simulation of pedestrian traffic flow. Transp. Res. B 28 (1994) 429–443. [CrossRef]
  35. B. Maury and J. Venel, Un modèle de mouvement de foule. ESAIM: Proc. 18 (2007) 143–152. [CrossRef] [EDP Sciences]
  36. B. Maury and J. Venel, Handling of contacts on crowd motion simulations, in Trafic and Granular Flow '07, Springer (2009) 171–180.
  37. B. Maury, A. Roudneff-Chupin and F. Santambrogio, A macroscopic crowd motion model of gradient flow type. Math. Mod. Meth. Appl. Sci. (to appear). Available at
  38. J.J. Moreau, Décomposition orthogonale d'un espace hilbertien selon deux cônes mutuellement polaires. C. R. Acad. Sci., Ser. I 255 (1962) 238–240.
  39. J.J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space. J. Diff. Equ. 26 (1977) 347–374. [CrossRef]
  40. K. Nagel, From particle hopping models to traffic flow theory. Transp. Res. Rec. 1644 (1998) 1–9. [CrossRef]
  41. P.D. Navin and R.J. Wheeler, Pedestrian flow characteristics. Traffic Engineering 39 (1969) 31–36.
  42. A. Schadschneider, Cellular automaton approach to pedestrian dynamics-theory, in Pedestrian and Evacuation Dynamics, M. Schreckenberg and S.D. Sharma Eds., Springer, Berlin (2001) 75–85.
  43. A. Schadschneider, A. Kirchner and K. Nishinari, From ant trails to pedestrian dynamics. Appl. Bionics & Biomechanics 1 (2003) 11–19. [CrossRef]
  44. G.K. Still, New computer system can predict human behavior response to building fires. Fire 84 (1993) 40–41.
  45. J. Venel, Modélisation mathématique et numérique des mouvements de foule. Ph.D. Thesis, Université Paris-Sud XI, France, available at: (2008).
  46. J. Venel, Integrating strategies in numerical modelling of crowd motion, in Pedestrian and Evacuation Dynamics '08, W.W.F. Klingsch, C. Rogsch, A. Schadschneider and M. Schreckenberg Eds., Springer, Berlin Heidelberg (2010) 641–646.
  47. J. Venel, Numerical scheme for a whole class of sweeping process. Available at: (submitted).
  48. U. Weidmann, Transporttechnik der fussgaenger. Technical Report 90, Schriftenreihe des Instituts für Verkehrsplanung, Transporttechnik, Strassen-und Eisenbahnbau, ETH Zürich, Switzerland (1993).
  49. S.J. Yuhaski and J.M. Macgregor Smith, Modelling circulation systems in buildings using state dependent queueing models. Queue. Syst. 4 (1989) 319–338. [CrossRef]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you