On Solving a Class of Continuous Traffic Equilibrium Problems and Planning Facility Location Under Congestion
Published Online:21 Mar 2022https://doi.org/10.1287/opre.2021.2213
References
- (2012) Dynamic simulation assignment model for pedestrian movements in crowded networks. Transportation Res. Record J. Transportation Res. Board 2316:95–105.Crossref, Google Scholar
- (1966) Complex Analysis (McGraw-Hill, New York).Google Scholar
- (2015) Reliable facility location design under service disruption, en-route congestion and in-facility queuing. Transportation Res. Part E Logist. Transportation Rev. 82:199–216.Crossref, Google Scholar
- (2017) Air taxis are about to take off. This one just did. NBC News (October 5), https://www.nbcnews.com/mach/science/air-taxis-are-about-take-one-just-did-ncna807416.Google Scholar
- (2016) Enhanced models and improved solution for competitive biofuel supply chain design under land use constraints. Eur. J. Oper. Res. 249(1):281–297.Crossref, Google Scholar
- (2011) Biofuel refinery location and supply chain planning under traffic congestion. Transportation Res. Part B Methodological 45(1):162–175.Crossref, Google Scholar
- BBC News (2015) Shanghai new year crush kills 36. BBC (January 1), https://www.bbc.com/news/world-asia-china-30646918.Google Scholar
- Bureau of Public Roads (1964) Traffic Assignment Manual, U.S. Dept. of Commerce, Urban Planning Division, Washington, DC.Google Scholar
- (2013) Euclidean hub-and-spoke networks. Oper. Res. 61(6):1360–1382.Link, Google Scholar
- (2015) Continuous facility location with backbone network costs. Transportation Sci. 49(3):433–451.Link, Google Scholar
- (2018) Uber just unveiled a prototype of its futuristic air taxi. NBC News (May 9), https://www.nbcnews.com/mach/science/uber-just-unveiled-prototype-its-futuristic-air-taxi-ncna872771.Google Scholar
- (2016) A multi-commodity discrete/continuum model for a traffic equilibrium system. Transportmetrica A Transportation Sci. 12(3):249–271.Crossref, Google Scholar
- (2014) A network optimization-based approach for crowd management in large public gatherings. Transportation Res. Part C Emerging Tech. 42:182–199.Crossref, Google Scholar
- (2014) Simulating the dynamic escape process in large public places. Oper. Res. 62(6):1344–1357.Link, Google Scholar
- (2011) Trajectory clustering and an application to airspace monitoring. IEEE Trans. Intelligent Transportation Systems. 12(4):1511–1524.Crossref, Google Scholar
- (2015) Death toll from Hajj stampede reaches 2,411 in new estimate. New York Times (December 10), https://www.nytimes.com/2015/12/11/world/middleeast/death-toll-from-hajj-stampede.html.Google Scholar
- (1996) Partial Differential Equations of Mathematical Physics and Integral Equations, Dover Books on Mathematics (Dover Publications, Mineola, NY).Google Scholar
- (2014) Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium. Transportation Res. Part B Methodological 63:38–52.Crossref, Google Scholar
- (2013) Integrated planning of supply chain networks and multimodal transportation infrastructure expansion: Model development and application to the biofuel industry. Comput. Aided Civil Infrastructure Engrg. 28(4):247–259.Crossref, Google Scholar
- (2005) Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions. Transportation Sci. 39(1):1–24.Link, Google Scholar
- (1995) Social force model for pedestrian dynamics. Physical Rev. E. 51(5):4282–4286.Crossref, Google Scholar
- (1993) Applied and Computational Complex Analysis, Discrete Fourier Analysis, Cauchy Integrals, Construction of Conformal Maps, Univalent Functions, vol. 3. (John Wiley & Sons, Hoboken, NJ).Google Scholar
- (2005) A Levenberg–Marquardt iterative solver for least-squares problems. Comm. Numer. Methods Engrg. 21(6):327–335.Crossref, Google Scholar
- (2006) Two-dimensional continuum modeling approach to transportation problems. J. Transportation Systems Engrg. Inform. Tech. 6(6):53–68.Crossref, Google Scholar
- (2003) A continuous traffic equilibrium model with multiple user classes. J. Eastern Asia Soc. Transportation Stud. 5:2831–2845.Google Scholar
- (2005) Pedestrian behavior at bottlenecks. Transportation Sci. 39(2):147–159.Link, Google Scholar
- (2011) Congestion pricing, heterogeneous users, and travel time reliability: Multicriterion dynamic user equilibrium model and efficient implementation for large-scale networks. Transportation Res. Record J. Transportation Res. Board 2254(1)58–67.Crossref, Google Scholar
- (2005) Optimizing the fundamental Neumann eigenvalue for the Laplacian in a domain with small traps. Eur. J. Appl. Math. 16(02):161–200.Crossref, Google Scholar
- (2011) Analysis of traffic congestion costs in a competitive supply chain. Transportation Res. Part E Logist. Transportation Rev. 47(1):1–17.Crossref, Google Scholar
- (2012) Competitive multi-facility location games with non-identical firms and convex traffic congestion costs. Transportation Res. Part E Logist. Transportation Rev. 48(1):373–385.Crossref, Google Scholar
- (2012) Shelter location and transportation planning under hurricane conditions. Transportation Res. Part E Logist. Transportation Rev. 48(4):715–729.Crossref, Google Scholar
- (2019) Link-based system optimum dynamic traffic assignment problems in general networks. Oper. Res. 67(1):167–182.Link, Google Scholar
- (1993) An investigation of the reliability of real-time information for route choice decisions in a congested traffic system. Transportation 20(2):157–178.Crossref, Google Scholar
- (2003) Vector Calculus (Macmillan, New York).Google Scholar
- (2014) Verification and validation of Viswalk for building evacuation modelling. Master thesis, Department of Fire Safety Engineering, Lund University, Sweden.Google Scholar
- (2011) Laplacian Eigenstructure of the Equilateral Triangle (Hikari, Limited, Rousse, Bulgaria).Google Scholar
- (2015) Facility location design under continuous traffic equilibrium. Transportation Res. Part B Methodological 81:18–33.Crossref, Google Scholar
- (2010) Numerical Conformal Mapping: Domain Decomposition and the Mapping of Quadrilaterals (World Scientific, Hackensack, NJ).Crossref, Google Scholar
- (1995) System optimal and user equilibrium time-dependent traffic assignment in congested networks. Ann. Oper. Res. 60(1):81–113.Crossref, Google Scholar
- (2017) Pedestrian assessment of a new football stadium in Zürich, Switzerland. Unpublished bachelor’s thesis, Hämeen ammattikorkeakoulu.Google Scholar
- PTV (2014) Ptv Vissim 7 User Manual (Karlsruhe, Germany).Google Scholar
- (2018) Check out the Uber air flying car that will transport passengers of the future. Fortune (May 8), https://fortune.com/2018/05/08/uber-air-flying-car-drone-video/.Google Scholar
- Reuters (2018) Chinese spend more on restaurants, movies, travel during new year holiday. Reuters (February 21), https://www.reuters.com/article/us-china-economy-consumer-idUSKCN1G51VC.Google Scholar
- (1982) Green’s Functions, vol. 239 (Cambridge University Press, Cambridge, UK).Google Scholar
- (2021) Efficiency of UAV-based last-mile delivery under congestion in low-altitude air. Transportation Res. Part C Emerging Tech. 122:102878–102891.Crossref, Google Scholar
- (1991) A location-allocation model and algorithm for evacuation planning under hurricane/flood conditions. Transportation Res. Part B Methodological 25(6):439–452.Crossref, Google Scholar
- (2010) Methods for measuring pedestrian density, flow, speed and direction with minimal scatter. Physica A. 389(9):1902–1910.Crossref, Google Scholar
- (1983) State of the art-location on networks: A survey. Part I: The p-center and p-median problems. Management Sci. 29(4):482–497.Link, Google Scholar
- (2018) People are now flying around in autonomous drones. CNN Business (February 8), https://money.cnn.com/2018/02/08/technology/ehang-self-flying-drone/index.html.Google Scholar
- Wang Z (2018) Planning service facilities and infrastructures under continuous traffic equilibrium. PhD dissertation, University of Illinois at Urbana-Champaign.Google Scholar
- (2021) Planning facility location in a continuous space under congestion and disruption risks. Working paper, University of Illinois at Urbana-Champaign.Google Scholar
- (1952) Road paper. Some theoretical aspects of road traffic research. Proc. Institution Civil Engineers 1(3):325–362.Crossref, Google Scholar
- (2018) Queuing analysis using Viswalk for check-in counter: Case study of Lombok Praya international airport. MATEC Web Conf. 181:2006–2018.Google Scholar
- (1996) Multivariable Mathematics (Prentice Hall, Upper Saddle River, NJ).Google Scholar
- (2001) A combined distribution and assignment model for continuous facility location problem. Ann. Regional Sci. 35(2):267–281.Crossref, Google Scholar
- (2004) Improved solution algorithm for multicommodity continuous distribution and assignment model. J. Urban Planning Development 130(1):14–23.Crossref, Google Scholar
- (1996) A spatial price equilibrium model with congestion effects. Ann. Regional Sci. 30(4):359–371.Crossref, Google Scholar
- (2000) A continuous equilibrium model for estimating market areas of competitive facilities with elastic demand and market externality. Transportation Sci. 34(2):216–227.Link, Google Scholar
- (1994) Traffic assignment in a congested discrete/continuous transportation system. Transportation Res. Part B Methodological 28(2):161–174.Crossref, Google Scholar
- (2020) Beijing’s five major railway stations deliver 600,000 passengers a day. Beijing Youth Daily (January 23), https://news.sina.cn/gn/2020-01-23/detail-iihnzahk5884470.d.html.Google Scholar
- (2021) Paved guideway topology optimization for pedestrian traffic under Nash equilibrium. Structural Multidisciplinary Optim. 63(3):1405–1426.Crossref, Google Scholar

