Abstract
Time-continuous models need to set a value of time-step to simulate a process using a computer. The assumed size of a time-step influences the computational performance. But not only a quick calculations is a criterion. The other one is the reliability of the simulation results. The discretization of time in computer simulation of pedestrian movement is considered in the paper. We consider a discrete-continuous approach which is becoming popular nowadays. Both aspects are investigated for the time-continuous SigmaEva pedestrian dynamics model. We use fundamental diagrams as a measure to estimate the simulation quality. It is shown that short and long time-steps are not reasonable.
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References
Baglietto G, Parisi DR (2011) Continuous-space automaton model for pedestrian dynamics. Phys. Rev. E 83:056117. https://doi.org/10.1103/PhysRevE.83.056117
Bandini S, Rubagotti F, Vizzari G, Shimura K (2011) A cellular automata based model for pedestrian and group dynamics: Motivations and first experiments. In: Malyshkin V (ed) Parallel Computing Technologies. Springer, Berlin Heidelberg, Berlin, Heidelberg, pp 125–139
Blue VJ, Adler JL (2001) Cellular automata microsimulation for modeling bi-directional pedestrian walkways. Transport Res Part B: Methodol 35(3):293–312. https://doi.org/10.1016/S0191-2615(99)00052-1
Chattaraj U, Seyfried A, Chakroborty P (2009) Comparison of pedestrian fundamental diagram across cultures. Adv Complex Sys 12(03):393–405. https://doi.org/10.1142/S0219525909002209
Chraibi M, Seyfried A, Schadschneider A (2010) Generalized centrifugal-force model for pedestrian dynamics. Phys. Rev. E 82:046111. https://doi.org/10.1103/PhysRevE.82.046111
Davidich M, Geiss F, Mayer HG, Pfaffinger A, Royer C (2013) Waiting zones for realistic modelling of pedestrian dynamics: A case study using two major German railway stations as examples. Transport Res Part C: Emerging Technol 37:210–222. https://doi.org/10.1016/j.trc.2013.02.016
Dridi M (2015) Simulation of high density pedestrian flow: a microscopic model. Open J Model Simulat 3:81–95. https://doi.org/10.4236/ojmsi.2015.33009
Geoerg P, Berchtold F, Gwynne S, Boyce K, Holl S, Hofmann A (2019) Engineering egress data considering pedestrians with reduced mobility. Fire Mater 43(7):759–781. https://doi.org/10.1002/fam.2736
Gravit M, Kirik E, Savchenko E (2021) Effect of design on the evacuation time for the colosseum of Rome. Construct Unique Buildings Struct 95:9504. https://doi.org/10.4123/CUBS.95.4
Gwynne SMV, Rosenbaum ER (2016) Employing the Hydraulic Model in Assessing Emergency Movement. 2115–2151. Springer New York, New York, NY . https://doi.org/10.1007/978-1-4939-2565-0_59
Hankin BD, Wright RA (1958) Passenger flow in subways. J Operat Res Soc 9(2):81–88. https://doi.org/10.1057/jors.1958.9
Helbing D, Farkas I, Vicsek T (2000) Simulating dynamical features of escape panic. Nature 407:487–490. https://doi.org/10.1038/35035023
Helbing D, Molnár P (1995) Social force model for pedestrian dynamics. Phys Rev E 51:4282–4286. https://doi.org/10.1103/PhysRevE.51.4282
Khan SD (2019) Congestion detection in pedestrian crowds using oscillation in motion trajectories. Eng Applicat Artificial Intell 85:429–443. https://doi.org/10.1016/j.engappai.2019.07.009
Khan SD, Vizzari G, Bandini S (2016) A Computer Vision Tool Set for Innovative Elder Pedestrians Aware Crowd Management Support Systems. In: AI*AAL@AI*IA, 75–91
Kholshevnikov V, Shields T, Boyce K, Samoshin D (2008) Recent developments in pedestrian flow theory and research in Russia. Fire Safety J 43(2):108–118. https://doi.org/10.1016/j.firesaf.2007.05.005
Kirchner A, Klupfel H, Nishinari K, Schadschneider A, Schreckenberg M (2004) Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics. J Statist Mechan: Theory Exp 2004(10):P10011. https://doi.org/10.1088/1742-5468/2004/10/p10011
Kirchner A, Schadschneider A (2002) Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics. Physica A: Statist Mechan Appl 312(1):260–276. https://doi.org/10.1016/S0378-4371(02)00857-9
Kirik E, Malyshev A, Popel E (2014) Fundamental diagram as a model input: Direct movement equation of pedestrian dynamics. In: Weidmann U, Kirsch U, Schreckenberg M (eds) Pedestrian and Evacuation Dynamics 2012. Springer International Publishing, Cham, pp 691–702
Kirik E, Malyshev A, Vitova T, Popel E, Kharlamov E (2018) Pedestrian movement simulation for stadiums design. IOP Conference Series: Materials Science and Engineering 456:012074. https://doi.org/10.1088/1757-899x/456/1/012074
Kirik E, Vitova T (2016) On formal presentation of update rules, density estimate and using floor fields in ca ff pedestrian dynamics model sigma.ca. In: S. El Yacoubi, J. Was, S. Bandini (eds.) Cellular Automata, pp. 435–445. Springer International Publishing, Cham . https://doi.org/10.1007/978-3-319-44365-2_43
Kirik E, Vitova T, Malyshev A (2019) Turns of different angles and discrete-continuous pedestrian dynamics model. Nat Comput 18:875–884. https://doi.org/10.1007/s11047-019-09764-4
Kirik E, Vitova T, Malyshev A, Popel E (2020) A conjunction of the discrete-continuous pedestrian dynamics model sigmaeva with fundamental diagrams. In: R. Wyrzykowski, E. Deelman, J. Dongarra, K. Karczewski (eds.) Parallel Processing and Applied Mathematics. 457–466. Springer International Publishing, Cham . https://doi.org/10.1007/978-3-030-43222-5_40
Kirik E, Vitova T, Malyshev A, Popel E, Kharlamov E, Moiseichenko V, Kalinin E, Smirnov N (2021) Computer simulation of pedestrian dynamics in the design and operation of stadiums. Construct Unique Build Struct 94:9401. https://doi.org/10.4123/CUBS.94.1
Kirik E, Yurgel’Yan T, Krouglov D (2011) On realizing the shortest time strategy in a ca ff pedestrian dynamics model. Cybernetics Syst 42(1):1–15. https://doi.org/10.1080/01969722.2011.532636
Kretz T (2019) An overview of fundamental diagrams of pedestrian dynamics . https://doi.org/10.13140/RG.2.2.30070.96326
Kuligowski ED (2016) Computer Evacuation Models for Buildings. 2152–2180. Springer New York, New York, NY . https://doi.org/10.1007/978-1-4939-2565-0_60
Mitsopoulou M, Dourvas N, Georgoudas IG, Sirakoulis GC (2020)Cellular automata model for crowd behavior management in airports. In: R. Wyrzykowski, E. Deelman, J. Dongarra, K. Karczewski (eds.) Parallel Processing and Applied Mathematics. 445–456. Springer International Publishing, Cham . https://doi.org/10.1007/978-3-030-43222-5_39
Nishinari K, Kirchner A, Namazi A, Schadschneider A (2003) Extended floor field ca model for evacuation dynamics. IEICE Transactions 87-D, 726–732
Ronchi E, Uriz FN, Criel X, Reilly P (2016) Modelling large-scale evacuation of music festivals. Case Studies in Fire Safety 5:11–19. https://doi.org/10.1016/j.csfs.2015.12.002
Schadschneider A, Seyfried A (2009) Validation of ca models of pedestrian dynamics with fundamental diagrams. Cybernet Syst 40(5):367–389. https://doi.org/10.1080/01969720902922400
Seitz MJ, Köster G (2012) Natural discretization of pedestrian movement in continuous space. Phys. Rev. E 86:046108. https://doi.org/10.1103/PhysRevE.86.046108
Seyfried A, Steffen B, Lippert T (2006) Basics of modelling the pedestrian flow. Physica A: Statist Mechan Applicat 368(1):232–238. https://doi.org/10.1016/j.physa.2005.11.052
Shimura K, Khan S, Bandini S, Nishinari K (2016) Simulation and evaluation of spiral movement of pedestrians: towards the tawaf simulator. J Cell Automata 11(4):275–284
Spearpoint M, MacLennan HA (2012) The effect of an ageing and less fit population on the ability of people to egress buildings. Safety Science 50(8), 1675–1684 . https://doi.org/10.1016/j.ssci.2011.12.019. Evacuation and Pedestrian Dynamics
Trivedi A, Pandey M (2020) Agent Based Modelling and Simulation to estimate movement time of pilgrims from one place to another at Allahabad Jn. Railway Station during Kumbh Mela-2019. Autonomous Agents and Multi-Agent Systems 34(1), 30 . https://doi.org/10.1007/s10458-020-09454-x
Vanumu LD, Ramachandra Rao K, Tiwari G (2017) Fundamental diagrams of pedestrian flow characteristics: a review. Eu Trans Res Rev 9(4):49. https://doi.org/10.1007/s12544-017-0264-6
Wang WL, Lo SM, Liu SB, Ma J (2015) On the use of a pedestrian simulation model with natural behavior representation in metro stations. Procedia Comput Sci 52:137–144. https://doi.org/10.1016/j.procs.2015.05.048
Weidmann U (1992) Transporttechnik der fussgänger. transporttechnische eigenschaften des fussgängerverkehrs (literaturauswertung). Tech. rep., Zürich. https://doi.org/10.3929/ethz-a-000687810
Zeng W, Nakamura H, Chen P (2014) A modified social force model for pedestrian behavior simulation at signalized crosswalks. Procedia -Soc Behavioral Sci 138:521–530. https://doi.org/10.1016/j.sbspro.2014.07.233
Zeng Y, Song W, Huo F, Vizzari G (2018) Modeling evacuation dynamics on stairs by an extended optimal steps model. Simulation Model Prac Theo 84:177–189. https://doi.org/10.1016/j.simpat.2018.02.001
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Kirik, E., Vitova, T. Time discretization in the time-continuous pedestrian dynamics model SigmaEva. Nat Comput 21, 407–415 (2022). https://doi.org/10.1007/s11047-022-09894-2
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DOI: https://doi.org/10.1007/s11047-022-09894-2
Keywords
- Pedestrian simulation
- Discrete-continuous model
- Fundamental diagram
- Flow rate
- Time discretization
- Time-step
- Person's size