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Cell-Based Dynamic Equilibrium Models

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Advances in Dynamic Network Modeling in Complex Transportation Systems

Part of the book series: Complex Networks and Dynamic Systems ((CNDS,volume 2))

Abstract

Cell-based dynamic equilibrium models are one class of dynamic traffic assignment (DTA) models that can capture equilibrium conditions and realistic traffic dynamics, such as queue spillback, queue formulation, and queue dissipation. However, compared with point-queue DTA models or DTA models using whole-link delay models for flow propagation, cell-based equilibrium models are often more computational demanding. This may raise issues for actual applications, in particular, for the implementation for real-time traffic control and route guidance applications, because the solution must be obtained quickly. Moreover, recent cell-based dynamic equilibrium models tend to capture more realistic travel behavior and traffic dynamics but this made the resulting models even more complicated and more difficult to solve for optimal solutions. Hence, this article aims at reviewing the recent development of cell-based dynamic equilibrium models, the formulation approaches, solution methods used, and the components of these models so as to point out the implementation issues of the latest cell-based dynamic equilibrium model with the consideration supply stochasticity for traffic control and route guidance applications as well as some gaps for future research directions.

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References

  • Ban X, Liu HX, Ferris MC, Ran B. A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. Transport Res. 2008;42B:823–842.

    Article  Google Scholar 

  • Bar-Gera H. Origin-based algorithm for the traffic assignment problem. Transport Sci. 2002;36:398–417.

    Article  Google Scholar 

  • Ben-Akiva M, Cuneo D, Hasan M, Jha M, Yang Q. Evaluation of freeway control using a microscopic simulation laboratory. Transport Res. 2003;11C:29–50.

    Google Scholar 

  • Carey M. Optimal time-varying flows on congested networks. Oper Res. 1987;35:58–69.

    Article  Google Scholar 

  • Cascetta E, Nuzzolo A, Russo F, Vitetta A. A modified logit route choice model overcoming path overlapping problems: specification and some calibration results for interurban networks. In: Lesort JB, editor, Transportation and traffic theory. New York: Pergamon; 1996. pp. 697–711.

    Google Scholar 

  • Chow AHF. Properties of system optimal traffic assignment with departure time choice and its solution method. Transport Res. 2009;43B:325–344.

    Article  Google Scholar 

  • Courant R, Friedrichs K, Lewy H. Ãœber die partiellen differenzengleichungen der mathematischen physik. Math Ann. 1967;100:32–74.

    Article  Google Scholar 

  • Daganzo CF. The cell transmission model: a simple dynamic representation of highway traffic. Transport Res. 1994;28B:269–287.

    Article  Google Scholar 

  • Daganzo CF. The cell transmission model, part ii: network traffic. Transport Res. 1995;29B:79–93.

    Article  Google Scholar 

  • Daganzo CF. The lagged cell transmission model. In: Ceder A, editor, Transportation and traffic theory. New York: Pergamon-Elservier; 1999. pp. 81–103.

    Google Scholar 

  • Daganzo CF. On the variational theory of traffic flow: well-posedness, duality and applications. Network Heterogeneous Media. 2006;1:601–619.

    Google Scholar 

  • Daganzo CF, Laval JA. On the numerical treatment of moving bottlenecks. Transport Res. 2005;39B:31–46.

    Article  Google Scholar 

  • Daganzo CF, Sheffi Y. On stochastic models of traffic assignment. Transport Sci. 1977;11:253–274.

    Article  Google Scholar 

  • Dial RB. A probabilistic multipath traffic assignment model which obviates path enumeration. Transport Res. 1971;5:83–111.

    Article  Google Scholar 

  • Doan K, Ukkusuri S. On the holding back problem in cell transmission based dynamic traffic assignment models. Transp. Res. Part B. 2012:1218–1238.

    Google Scholar 

  • Friesz TL, Bernstein DH, Smith TE, Tobin RL, Wie BW. A variational inequality formulation of the dynamic network user equilibrium problem. Oper Res. 1993;41:179–191.

    Article  Google Scholar 

  • Golani H, Waller ST. Combinatorial approach for multi-destination dynamic traffic assignment. J Transport Res Board. 2004;1882:70–78.

    Google Scholar 

  • Han D, Lo HK. A new alternating direction method for a class of nonlinear variational inequality problems. J Optim Theor Appl. 2002;112:549–560.

    Article  Google Scholar 

  • Han D, Lo HK. Solving nonadditive traffic assignment problems: a decent method for co-coercive variational inequalities. Eur J Oper Res. 2004;159:529–544.

    Article  Google Scholar 

  • Han L, Ukkusuri S, Doan K. Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity. Transp Res B. 2011;45:1749–1767.

    Article  Google Scholar 

  • Ho J. A successive linear optimization approach to the dynamic traffic assignment problem. Transport Sci. 1980;14:295–305.

    Article  Google Scholar 

  • Jackson WB, Jucker JV. An empirical study of travel time variability and travel choice behavior. Transport Sci. 1982;16:460–475.

    Article  Google Scholar 

  • Jayakrishnan R, Tsai WK, Chen A. A dynamic traffic assignment model with traffic flow relationship. Transport Res. 1995;3C:51–82.

    Google Scholar 

  • Lam WHK, Huang HJ. Dynamic user optimal traffic assignment model for many to one travel demand. Transport Res. 1995;29B:243–259.

    Article  Google Scholar 

  • Leclercq L. Bounded acceleration close to fixed and moving bottlenecks. Transport Res. 2007;41B:309–319.

    Article  Google Scholar 

  • Li Y, Waller ST, Ziliaskopoulos AK. A decomposition scheme for system optimal dynamic traffic assignment models. Network Spatial Econ. 2003;3:441–455.

    Article  Google Scholar 

  • Li Y, Ziliaskopoulos AK, Waller ST. Linear programming formulations for system optimum dynamic traffic assignment with arrival time based and departure time based demands. J Transport Res Board. 1999;1667:52–59.

    Article  Google Scholar 

  • Lighthill MJ, Whitham JB. On kinematic waves. I. Flow movement in long rivers. II. A theory of traffic flow on long crowded road. Proc R Soc. 1955;A229:281–345.

    Google Scholar 

  • Lin WH, Wang C. An enhanced 0–1 mixed-integer LP formulation for traffic signal control. IEEE Trans Intell Transport Syst. 2004;5:238–245.

    Article  Google Scholar 

  • Liu HX, He XZ, He BS. Method of Successive Weighted Averages (MSWA) and self-regulated averaging schemes for solving stochastic user equilibrium problem. Network Spatial Econ. 2009;9:485–503.

    Article  Google Scholar 

  • Lo HK, Luo XW, Siu BWY. Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion. Transp Res Part B: Methodol. 2006;40(9):792–806.

    Article  Google Scholar 

  • Lo HK. A dynamic traffic assignment formulation that encapsulates the cell-transmission model. In: Ceder A, editor. Transportation and traffic theory. Oxford: Elsevier; 1999. pp. 327–350.

    Google Scholar 

  • Lo HK. A cell-based traffic control formulation: strategies and benefits of dynamic plans. Transport Sci. 2001;35:148–164.

    Article  Google Scholar 

  • Lo HK, Chen A. Traffic equilibrium problem with route-specific costs: formulation and algorithms. Transport Res. 2000;34B:493–513.

    Article  Google Scholar 

  • Lo HK, Szeto WY. A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transport Res. 2002a;36B:421–443.

    Article  Google Scholar 

  • Lo HK, Szeto WY. A cell-based dynamic traffic assignment model: formulation and properties. Math Comput Model. 2002b;35:849–865.

    Article  Google Scholar 

  • Lo HK, Szeto WY. Modeling advanced traveler information services: static versus dynamic paradigms. Transport Res. 2004;38B:495–515.

    Article  Google Scholar 

  • Mahmassani HS, Liu YH. Models of user pre-trip and en-route switching decisions in response to real-time information. Transportation systems 1997. (TS’97). Proceedings volume from the 8th IFAC/IFIP/IFORS Symposium. 1997;3:1363–1368.

    Google Scholar 

  • Munoz L, Sun X, Horowitz R, Alvarez L. Traffic density estimation with the cell transmission model, Proceedings of the American Control Conference, Denver, Colorado, June, 2003. 3750–3755.

    Google Scholar 

  • Nagurney A. Network economics: a variational inequality approach. Norwell, MA: Kluwer Academic; 1993.

    Book  Google Scholar 

  • Ngoduy D. Multiclass first order model using stochastic fundamental diagrams. Transportmetrica. 2011;7:111–125.

    Article  Google Scholar 

  • Nie Y. A cell-based merchant–nemhauser model for the system optimum dynamic traffic assignment problem. Transp Res B. 2011;45:329–342.

    Article  Google Scholar 

  • Nie Y, Zhang HM. Solving the dynamic user optimal assignment problem considering queue spillback. Network Spatial Econ. 2010;10:49–71.

    Article  Google Scholar 

  • Pan T, Sumalee A, Zhong R, Uno N. The stochastic cell transmission model considering spatial and temporal correlations for traffic states prediction. Proceedings of the third international symposium on dynamic traffic assignment 2010.

    Google Scholar 

  • Pavlis Y, Recker W. A mathematical logic approach for the transformation of the linear conditional piecewise functions of dispersion-and-store and cell transmission traffic flow models into linear mixed-integer form. Transport Sci. 2009;43:98–116.

    Article  Google Scholar 

  • Peeta S, Ziliaskopoulos AK. Foundations of dynamic traffic assignment: the past, the present and the future. Network Spatial Econ. 2001;1:233–265.

    Article  Google Scholar 

  • Ramadurai G, Ukkusuri SV. Dynamic user equilibrium model for combined activity-travel choices using activity-travel supernetwork representation. Network Spatial Econ. 2010;10:273–292.

    Article  Google Scholar 

  • Ramadurai G. Novel dynamic user equilibrium models: analytical formulations, multi-dimensional choice, and an efficient algorithm. Ph.D. Thesis, Department of civil and environmental engineering. Troy, NY: Rensselaer Polytechnic Institute; 2009.

    Google Scholar 

  • Ramadurai G, Ukkusuri SV, Zhao S, Pang JS. Linear complementarity formulation for single bottleneck model with heterogeneous commuters. Transp Res B. 2010;44:193–214.

    Article  Google Scholar 

  • Ran B, Boyce D. Modeling dynamic transportation networks. An intelligent transportation system oriented approach, 2nd revised edn. Heidelberg: Springer; 1996.

    Book  Google Scholar 

  • Ran B, Lee DH, Shin MSI. Dynamic traffic assignment with rolling horizon implementation. J Transport Eng. 2002;128:314–322.

    Article  Google Scholar 

  • Richards PI. Shockwaves on the highway. Oper Res. 1956;4:42–51.

    Article  Google Scholar 

  • Shao H, Lam WHK, Tam ML. A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand. Network Spatial Econ. 2006;6:173–204.

    Article  Google Scholar 

  • Sharma S, Mathew TV, Ukkusuri SV. Approximation techniques for transportation network design problem under demand uncertainty. J Comput Civ Eng. 2011;25:316–329.

    Article  Google Scholar 

  • Shen W, Nie YM, Zhang H. Dynamic network simplex method for designing emergency evacuation plans. Transport Res Rec. 2007;2022:83–93.

    Google Scholar 

  • Simon H. A behavioural model of rational choice. Q J Econ. 1955;69:99–118.

    Article  Google Scholar 

  • Small KA. The scheduling of consumer activities: work trips. Am Econ Rev. 1982;72:467–479.

    Google Scholar 

  • Sumalee A, Zhong RX, Pan TL, Szeto WY. Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment. Trans Res B. 2011;45:507–533.

    Article  Google Scholar 

  • Sumalee A, Zhong RX, Pan TL, Iryo T, Lam WHK. Stochastic cell transmission model for traffic network with demand and supply uncertainties. Transport Res B. 2010;45:507–533.

    Article  Google Scholar 

  • Sumalee A, Zhong R, Szeto WY, Pan T. Stochastic cell transmission model under demand and supply uncertainties. Proceedings of the second international symposium on dynamic traffic assignment 2008.

    Google Scholar 

  • Szeto WY. The enhanced lagged cell-transmission model for dynamic traffic assignment. Transport Res Rec. 2008;2085:76–85.

    Google Scholar 

  • Szeto WY, Lo HK. A cell-based simultaneous route and departure time choice model with elastic demand. Transport Res. 2004;38B:593–612.

    Article  Google Scholar 

  • Szeto WY, Lo HK. The impact of advanced traveler information services on travel time and schedule delay costs. J Intell Transport Syst Tech Plan Oper. 2005;9:47–55.

    Article  Google Scholar 

  • Szeto WY, Lo HK. Dynamic traffic assignment: properties and extensions. Transportmetrica. 2006;2:31–52.

    Article  Google Scholar 

  • Szeto WY, Sumalee A. Multi-class reliability-based stochastic-dynamic-user-equilibrium assignment problem with random traffic states. Proceedings of the 88th annual meeting of transportation research board. 2009.

    Google Scholar 

  • Szeto WY, Ghosh B, Basu B, O’Mahony M. Cell-based short-term traffic flow forecasting using time series modelling. ASCE J Transport Eng. 2009;135:658–667.

    Article  Google Scholar 

  • Szeto WY, Sumalee A, Jiang Y. A cell-based model for multi-class doubly stochastic dynamic traffic assignment. Comput Aided Civ Infrastruct Eng. 2011;26:595–611.

    Article  Google Scholar 

  • Ukkusuri S. Linear programs for user optimal dynamic traffic assignment problem. Master’s thesis, University of Illinois at Urbana Champaign. 2002.

    Google Scholar 

  • Ukkusuri S, Han L, Doan K. Dynamic user equilibrium with a path based cell transmission model for general traffic networks. Transp Res B. 2012;46:1657–1684.

    Article  Google Scholar 

  • Ukkusuri SV, Waller ST. Linear programming models for the user optimal and system optimal network design problem: formulations, comparisons and extensions. Network Spatial Econ. 2008;8:383–406.

    Article  Google Scholar 

  • Waller ST, Ziliaskopoulos AK. A combinatorial user optimal dynamic traffic assignment algorithm. Ann Oper Res. 2006;144:249–261.

    Article  Google Scholar 

  • Wardrop J. Some theoretical aspects of road traffic research. Proceedings of the institute of civil engineers, Part II. 1952;325–378.

    Google Scholar 

  • Wie BW, Tobin RL, Friesz TL. The augmented lagrangian method for solving dynamic network traffic assignment models in discrete-time. Transport Sci. 1994;28:204–220.

    Article  Google Scholar 

  • Wong SC, Wong CK, Tong CO. A parallelized genetic algorithm for calibration of lowry model. Parallel Comput. 2001;27:1523–1536.

    Article  Google Scholar 

  • Yang H, Meng Q. Departure time, route choice and congestion toll in a queuing network with elastic demand. Transport Res. 1998;32B:247–260.

    Article  Google Scholar 

  • Zhang L, Yin Y, Lou Y. Robust signal timing for arterials under day-to-day demand variations. Transp Res Record, 2010;2192:156–166.

    Article  Google Scholar 

  • Zheng H, Chang YC. A network flow algorithm for the cell-based single-destination system optimal dynamic traffic assignment problem. Transport Sci. 2011;45:121–137.

    Article  Google Scholar 

  • Ziliaskopoulos AK. A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transport Sci. 2000;34:37–49.

    Article  Google Scholar 

  • Ziliaskopoulos AK, Rao L. A simultaneous route and departure time choice equilibrium model on dynamic networks. Int Trans Oper Res. 1999;6:21–37.

    Article  Google Scholar 

  • Ziliaskopoulos AK, Waller ST, Li Y, Byram M. Large-scale dynamic traffic assignment: implementation issues and computational analysis. J Transport Eng ASCE. 2004;130:585–593.

    Article  Google Scholar 

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Acknowledgements

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 716312E). The author is grateful for the two reviewers for their constructive comments.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Hong Kong, Hong Kong, Hong Kong

    W. Y. Szeto

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  1. W. Y. Szeto
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Correspondence to W. Y. Szeto .

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Editors and Affiliations

  1. , School of Civil Engineering, Purdue University, Stadium Mall Drive 550, West Lafayette, 47907, USA

    Satish V. Ukkusuri

  2. , Department of Civil & Environmental Engi, Rutgers University, Browser Road 623, Piscataway, 08854, New Jersey, USA

    Kaan Ozbay

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Szeto, W.Y. (2013). Cell-Based Dynamic Equilibrium Models. In: Ukkusuri, S., Ozbay, K. (eds) Advances in Dynamic Network Modeling in Complex Transportation Systems. Complex Networks and Dynamic Systems, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6243-9_7

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