zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the modeling of pedestrian motion. (English) Zbl 1185.90038
Summary: A model for the simulation of pedestrian flows and crowd dynamics has been developed. The model is based on a series of forces, such as: will forces (the desire to reach a place at a certain time), pedestrian collision avoidance forces, obstacle/wall avoidance forces; pedestrian contact forces, and obstacle/wall contact forces. Except for the will force, it is assumed that for any given pedestrian these forces are the result of only local (nearest neighbour) situations. The near-neighbour search problem is solved by an efficient incremental Delaunay triangulation that is updated at every timestep. In order to allow for general geometries a so-called background triangulation is used to carry all geographic information. At any given time the location of any given pedestrian is updated on this mesh. The results obtained to date show that the model performs well for standard benchmarks, and allows for typical crowd dynamics, such as lane forming, overtaking, avoidance of obstacles and panic behaviour.

90B20Traffic problems
91D10Models of societies, social and urban evolution
37N99Applications of dynamical systems
65D17Computer aided design (modeling of curves and surfaces)
Full Text: DOI
[1] Deere, S. J.; Galea, E. R.; Lawrence, P. J.: A systematic methodology to assess the impact of human factors in ship design, Appl. math. Modell. 33, No. 2, 867-883 (2009)
[2] Zheng, X.; Zhong, T.; Liu, M.: Modeling crowd evacuation of a building based on seven methodological approaches, Build. environ. 44, 437-445 (2009)
[3] , Pedestrian and evacuation dynamics (2002) · Zbl 0976.00018
[4] Legion International Limited, Legion, <http://www.legion.biz/>.
[5] Hughes, R. L.: A continuum theory for the flow of pedestrians, Trans. res. Part B 36, 507-535 (2002)
[6] Hughes, R. L.: The flow of human crowds, Annu. rev. Fluid mech. 35, 169-182 (2003) · Zbl 1125.92324 · doi:10.1146/annurev.fluid.35.101101.161136
[7] Blue, V. J.; Adler-Emergent, J. L.: Fundamental pedestrian flows from cellular automata microsimulation, Trans. res. Rec. 1644, 29-36 (1998)
[8] Blue, V. J.; Adler-Flow, J. L.: Capacities from cellular automata modeling of proportional splits of pedestrians by direction, Pedestrian and evacuation dynamics, 115-122 (2002)
[9] Dijkstra, J.; Jesurun, J.; Timmermans, H.: A multi-agent cellular automata model of pedestrian movement, Pedestrian and evacuation dynamics, 173-180 (2002)
[10] Kessel, A.; Klüpfel, H.; Wahle, J.; Schreckenberg, M.: Microscopic simulation of pedestrian crowd motion, Pedestrian and evacuation dynamics, 193-202 (2002)
[11] Schadschneider, A.: Cellular automaton approach to pedestrian dynamics -- theory, Pedestrian and evacuation dynamics, 75-86 (2002)
[12] Isobe, M.; Adachi, T.; Nagatani, T.: Experiment and simulation of pedestrian counter flow, Physica A 336, 638-650 (2004)
[13] Helbing, D.; Molnar, P.: Social force model for pedestrian dynamics, Phys. rev. E 51, 42824286 (1995)
[14] Helbing, D.; Farkas, I. J.; Molnár, P.; Vicsek, T.: Simulation of pedestrian crowds in normal and evacuation situations, Pedestrian and evacuation dynamics, 21-58 (2002)
[15] Lakoba, T. I.; Kaup, D. J.; Finkelstein, N. M.: Modifications of the Helbing -- molnár -- farkas -- vicsek social force model for pedestrian evolution, Simulation 81, 339 (2005)
[16] Fruin, J. J.: Pedestrian planning and design, (1971)
[17] Young, S. B.: Evaluation of pedestrian walking speeds in airport terminals, Trans. res. Rec. 1674 (1999)
[18] Löhner, R.: Applied CFD techniques, (2008)
[19] Löhner, R.; Ambrosiano, J.: A vectorized particle tracer for unstructured grids, J. comput. Phys. 91, No. 1, 22-31 (1990) · Zbl 0718.65076 · doi:10.1016/0021-9991(90)90002-I
[20] Knuth, D. E.: The art of computer programming, The art of computer programming 1 -- 3 (1973) · Zbl 0895.68054
[21] Sedgewick, R.: Algorithms, (1983) · Zbl 0529.68002
[22] Munjiza, A.; Andrews, K. R. F.: NBS contact detection algorithm for bodies of similar size, Int. J. Numer. meth. Eng. 43, 131-149 (1998) · Zbl 0937.74079 · doi:10.1002/(SICI)1097-0207(19980915)43:1<131::AID-NME447>3.0.CO;2-S
[23] Munjiza, A.; Rougier, E.; John, N. W. M.: MR linear contact detection algorithm, Int. J. Numer. meth. Eng. 66, 46-71 (2006) · Zbl 1110.70302 · doi:10.1002/nme.1538
[24] Löhner, R.: The empty bin: a data structure for spatial search of time-varying data, Commun. numer. Meth. eng. 23, No. 12, 1111-1119 (2007) · Zbl 1127.74052 · doi:10.1002/cnm.959
[25] T. Kretz, A. Grünebohm, M. Schreckenberg, Experimental Study of Pedestrian Flow Through a Bottleneck, arXiv:physics/0610077v1, 11 October 2006.