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Evacuation modeling: a case study on linear and nonlinear network flow models

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EURO Journal on Computational Optimization

Abstract

We present a nonlinear traffic flow network model that is coupled to gaseous hazard information for evacuation planning. This model is evaluated numerically against a linear network flow model for different objective functions that are relevant for evacuation problems. A numerical study shows the influence of the underlying evacuation models on the evacuation time as well as the exit strategies.

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References

  • Ahuja R, Mananti T, Orlin J (1993) Network flows: theory, algorithms, and applications. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Bazzan AL, Klügl F (2014) A review on agent-based technology for traffic and transportation. Knowl Eng Rev 29(03):375–403

    Article  Google Scholar 

  • Borrmann A, Kneidl A, Köster G, Ruzika S, Thiemann M (2012) Bidirectional coupling of macroscopic and microscopic pedestrian evacuation models. Saf Sc 50(8):1695–1703

    Article  Google Scholar 

  • Burkard R, Dlaska K, Klinz B (1993) The quickest flow problem. Math Methods Oper Res 37:31–58

    Article  Google Scholar 

  • Chalmet L, Francis R, Saunders P (1982) Network models for building evacuation. Fire Technol 18(1):90–113

    Article  Google Scholar 

  • Chattaraj U, Seyfried A, Chakroborty P (2009) Comparison of pedestrian fundamental diagram across cultures. Adv Complex Syst 12(03):393–405

    Article  Google Scholar 

  • Choi W, Hamacher H, Tufekci S (1988) Modeling of building evacuation problems by network flows with side constraints. Eur J Oper Res 35(1):98–110

    Article  Google Scholar 

  • Coclite G, Garavello M, Piccoli B (2005) Traffic flow on a road network. SIAM J Math Anal 36(6):1862–1886

    Article  Google Scholar 

  • Crank J, Nicolson P (1947) A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type. In: Mathematical proceedings of the Cambridge Philosophical Society,vol 43. Cambridge Univ Press, pp 50–67

  • Dietrich F, Köster G, Seitz M, von Sivers I (2014) Bridging the gap: from cellular automata to differential equation models for pedestrian dynamics. J Comput Sci 5(5):841–846

    Article  Google Scholar 

  • Fleischer L, Tardos É (1998) Efficient continuous-time dynamic network flow algorithms. Oper Res Lett 23(3–5):71–80

    Article  Google Scholar 

  • Garavello M, Goatin P (2012) The Cauchy problem at a node with buffer. Discr Contin Dyn Syst Ser A (DCDS-A) 32(6):1915–1938

    Article  Google Scholar 

  • Göttlich S, Kolb O, Kühn S (2014) Optimization for a special class of traffic flow models: Combinatorial and continuous approaches. Netw Heterogen Med 9:315–334

  • Göttlich S, Kühn S, Ohst J, Ruzika S, Thiemann M (2011) Evacuation dynamics influenced by spreading hazardous material. Netw Heterogen Med (NHM) 6(3):443–464

    Article  Google Scholar 

  • Graat E, Midden C, Bockholts P (1999) Complex evacuation; effects of motivation level and slope of stairs on emergency egress time in a sports stadium. Saf Sci 31(2):127–141

    Article  Google Scholar 

  • Gwynne S, Galea E, Owen M, Lawrence P, Filippidis L (1999) A review of the methodologies used in evacuation modelling. Fire Mater 23:383–388

    Article  Google Scholar 

  • Hamacher H, Heller S, Köster G, Klein W (2010) A sandwich approach for evacuation time bounds. In: Proceedings of the 5th international conference on pedestrian and evacuation dynamics

  • Hamacher H, Klamroth K (2000) Linear and network optimization problems—Lineare und Netzwerk Optimierungsprobleme. Vieweg, Braunschweig

    Book  Google Scholar 

  • Hamacher H, Tjandra S (2002) Mathematical modelling of evacuation problems-a state of the art. In: Schreckenberger M, Sharma S (eds) Pedestrian and evacuation dynamics. Springer, Berlin, pp 227–266

    Google Scholar 

  • Helbing D (1991) A mathematical model for the behavior of pedestrians. J Behav Sci 36(4):298–310

    Article  Google Scholar 

  • Helbing D, Schreckenberg M (1999) Cellular automata simulating experimental properties of traffic flow. Phys Rev E 59:R2505–R2508

    Article  Google Scholar 

  • Herty M, Klar A (2003) Modeling, simulation, and optimization of traffic flow networks. SIAM J Sci Comput 25(3):1066–1087

    Article  Google Scholar 

  • Herty M, Lebacque JP, Moutari S (2009) A novel model for intersections of vehicular traffic flow. Netw Heterogen Med (NHM) 4(4):813–826

    Article  Google Scholar 

  • Hoogendoorn S, Bovy P (2000) Gas-kinetic modeling and simulation of pedestrian flows. Transp Res Rec J Transp Res Board (1710):28–36

  • Hughes R (2002) A continuum theory for the flow of pedestrians. Transp Res Part B 36:507–535

    Article  Google Scholar 

  • Jiang G, Levy D, Lin C, Osher S, Tadmor E (1998) High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws. SIAM J Numer Anal 35(6):2147–2168

    Article  Google Scholar 

  • Johansson F, Peterson A, Tapani A (2014) Local performance measures of pedestrian traffic. Public Transp 6(1–2):159–183

    Article  Google Scholar 

  • Klüpfel H, Schreckenberg M, Meyer-König T (2005) Models for crowd movement and egress simulation. In: Traffic and Granular Flow ’03, pp 357–372. Springer

  • Kneidl A, Thiemann M, Bormann A, Ruzika S, Hamacher H, Köster G, Rank E (2010) Bidirectional coupling of macroscopic and microscopic approaches for pedestrian behavior prediction. In: Proceedings of the 5th international conference on pedestrian and evacuation dynamics

  • Kolb O (2011) Simulation and optimization of gas and water supply networks. PhD Thesis, Technische Universität Darmstadt

  • Köster G, Hartmann D, Klein W (2011) Microscopic pedestrian simulations: From passenger exchange times to regional evacuation. In: Operations research proceedings 2010, pp 571–576. Springer

  • Krumke S, Noltemeier H (2005) Graphentheorische Konzepte und Algorithmen. B.G. Teubner, Stuttgart

    Book  Google Scholar 

  • Kühn S (2015) Continuous traffic flow models and their applications. Dr, Hut, Verlag

    Google Scholar 

  • LeVeque R (1992) Numerical methods for conservation laws, 2nd edn. Birkhäuser Verlag, Basel, Boston, Berlin

    Book  Google Scholar 

  • Nagel K, Flötteröd G (2012) Agent-based traffic assignment: Going from trips to behavioural travelers. In: Travel behaviour research in an evolving world–selected papers from the 12th international conference on travel behaviour research, pp 261–294

  • Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. Journal de physique I 2(12):2221–2229

    Article  Google Scholar 

  • Pandey G, Rao KR, Mohan D (2015) A review of cellular automata model for heterogeneous traffic conditions. In: Traffic and Granular Flow’13, Springer, pp 471–478

  • Rosen J, Sun SZ, Xue GL (1991) Algorithms for the quickest path problem and the enumeration of quickest paths. Comput Oper Res 18(6):579–584

    Article  Google Scholar 

  • Schadschneider A, Klingsch W, Klüpfel H, Kretz T, Rogsch C, Seyfried A (2009) Evacuation dynamics: empirical results, modeling and applications. In: Meyers B (ed) Encyclopedia of complexity and system science. Springer, New York, NY, pp 3142–3176

    Chapter  Google Scholar 

  • Seyfried A, Steffen B, Lippert T (2006) Basics of modelling the pedestrian flow. Phys A Stat Mech Appl 368(1):232–238

    Article  Google Scholar 

  • Southworth F (1991) Regional evacuation modeling: a state-of-the-art review. In: ORNL/TAM-11740. Oak Ridge National Laboratory, Energy Division, Oak Ridge, TN

  • Tian J, Treiber M, Zhu C, Jia B, Li H (2014) Cellular automaton model with non-hypothetical congested steady state reproducing the three-phase traffic flow theory. In: Cellular automata, Springer, pp 610–619

  • von Sivers I, Templeton A, Köster G, Drury J, Philippides A (2014) Humans do not always act selfishly: social identity and helping in emergency evacuation simulation. Transp Res Proc 2:585–593

    Article  Google Scholar 

  • Zanlungo F, Ikeda T, Kanda T (2011) Social force model with explicit collision prediction. EPL (Europhys Lett) 93(6):68,005

    Article  Google Scholar 

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Acknowledgments

The work of S. Kühn and J. P. Ohst was supported by Stiftung Rheinland-Pfalz für Innovation, Project EvaC, FKZ 989. S. Ruzika gratefully acknowledges support by the German Federal Ministry of Education and Research (BMBF), Reference Number 13N12825. This work was also financially supported by the German Academic Exchange Service (DAAD) project “Transport network modeling and analysis” (Project-ID 57049018).

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Göttlich, S., Kühn, S., Ohst, J.P. et al. Evacuation modeling: a case study on linear and nonlinear network flow models. EURO J Comput Optim 4, 219–239 (2016). https://doi.org/10.1007/s13675-015-0055-6

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  • DOI: https://doi.org/10.1007/s13675-015-0055-6

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