Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning

Abstract

This study proposes an analytical capacity constrained dynamic traffic assignment (DTA) model along with an efficient path-based algorithm. The model can be applied to analyzing dynamic traffic demand management (TDM) strategies, but its specific feature is allowing for an evaluation of advanced traveler information systems (ATIS) within the strategic transportation planning framework. It is an extension of a former DTA model, where each link is given an infinite capacity and is assumed to be completely traversed inside any time interval it is reach by a path. Thereby, the length of time intervals should be very longer than the link travel times, and the link capacity constraints are overlooked. The paper rests on three key ideas to overcome these restrictions: (1) adding path-link fraction variables to the base model, allowing path flows to spread out over time intervals on long links; (2) uniformly dividing each link into smaller parts (segments), so that each part is more likely to be traversed inside a time interval; (3) imposing a dynamic penalty function on each link, thereby the capacity constraint can be included. The proposed DTA algorithm decomposes the augmented model in terms of origin-destination (OD) pairs and departure time intervals, and utilizes a dynamic column generation technique for generating active paths between the OD pairs. The optimal solution to a one-link network demonstrates that the model is able to approximate the dynamic flow propagation over a link with sensible accuracy. Besides, investigation of the results for a small test network reveals that the algorithm performs very well in computing temporal link flows and queuing delays. Finally, numerical experiments on a real life network indicate that the algorithm converges sufficiently fast and provides path information for each time interval. The network is further used to show the algorithm is capable of assessing a dynamic TDM strategy as well as an ATIS system.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. Ban XJ, Liu HX, Ferris MC, Ran B (2008) A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. Transp Res B Methodol 42(9):823–842

    Article  Google Scholar 

  2. Beckmann M, McGuire CB, Winsten CB (1956) Studies in the economics of transportation. Published for the Cowles Commission for Research in Economics by Yale University Press, New Haven

    Google Scholar 

  3. Ben-Akiva M, Bierlaire M, Bottom J, Koutsopoulos H, Mishalani R (1997a) Development of a route guidance generation system for real-time application. In Proceedings of the IFAC Transportation Systems 97 Conference, Chania

  4. Ben-Akiva ME, Koutsopoulos HN, Mishalani RG, Yang Q (1997b) Simulation laboratory for evaluating dynamic traffic management systems. J Transp Eng 123(4):283–289

    Article  Google Scholar 

  5. Ben-Akiva ME, Gao S, Wei Z, Wen Y (2012) A dynamic traffic assignment model for highly congested urban networks. Transp Res C 24:62–82

    Article  Google Scholar 

  6. Bliemer MC, Raadsen MP, Brederode LJ, Bell MG, Wismans LJ, Smith MJ (2017) Genetics of traffic assignment models for strategic transport planning. Transp Rev 37(1):56–78

    Article  Google Scholar 

  7. Boyce DE, Lee DH, Janson BN, Berka S (1997) Dynamic route choice model of large-scale traffic network. J Transp Eng 123(4):276–282

    Article  Google Scholar 

  8. Carey M (1987) Optimal time-varying flows on congested networks. Oper Res 35(1):58–69

    Article  Google Scholar 

  9. Daganzo CF (1994) The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transp Res B Methodol 28(4):269–287

    Article  Google Scholar 

  10. Daganzo CF (1995) The cell transmission model, part II: network traffic. Transp Res B Methodol 29(2):79–93

    Article  Google Scholar 

  11. Florian M, Mahut M, Tremblay N (2008) Application of a simulation-based dynamic traffic assignment model. Eur J Oper Res 189(3):1381–1392

    Article  Google Scholar 

  12. Friesz TL, Bernstein D, Smith TE, Tobin RL, Wie BW (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper Res 41(1):179–191

    Article  Google Scholar 

  13. Friesz TL, Kim T, Kwon C, Rigdon MA (2011) Approximate network loading and dual-time-scale dynamic user equilibrium. Transp Res B Methodol 45(1):176–207

    Article  Google Scholar 

  14. Friesz TL, Han K, Neto PA, Meimand A, Yao T (2013) Dynamic user equilibrium based on a hydrodynamic model. Transp Res B Methodol 47:102–126

    Article  Google Scholar 

  15. Gentile G (2016) Solving a dynamic user equilibrium model based on splitting rates with gradient projection algorithms. Transp Res B Methodol 92:120–147

    Article  Google Scholar 

  16. Golden B (1976) Technical note—shortest-path algorithms: a comparison. Oper Res 24(6):1164–1168

    Article  Google Scholar 

  17. Han L, Ukkusuri S, Doan K (2011) Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity. Transp Res B Methodol 45(10):1749–1767

    Article  Google Scholar 

  18. Han K, Friesz TL, Yao T (2013a) A partial differential equation formulation of Vickrey’s bottleneck model, part I: methodology and theoretical analysis. Transp Res B Methodol 49:55–74

    Article  Google Scholar 

  19. Han K, Friesz TL, Yao T (2013b) A partial differential equation formulation of Vickrey’s bottleneck model, part II: numerical analysis and computation. Transp Res B Methodol 49:75–93

    Article  Google Scholar 

  20. Han K, Friesz TL, Yao T (2013c) Existence of simultaneous route and departure choice dynamic user equilibrium. Transp Res B Methodol 53:17–30

    Article  Google Scholar 

  21. Han K, Piccoli B, Szeto WY (2016) Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness. Transportmetrica B: Transp Dyn 4(3):187–222

  22. Han K, Eve G, Friesz TL (2019) Computing dynamic user equilibria on large-scale networks with software implementation. Netw Spat Econ 19(3):869–902

  23. Hearn DW, Ribera J (1980) Bounded flow equilibrium problems by penalty methods. In: Proceedings of IEEE International Conference on Circuits and Computers, p 162–166

  24. Janson BN (1991a) Dynamic traffic assignment for urban road networks. Transp Res B Methodol 25(2):143–161

    Article  Google Scholar 

  25. Janson BN (1991b) Convergent algorithm for dynamic traffic assignment. Transp Res Rec (1328):69–80

  26. Janson BN, Robles J (1995) Quasi-continuous dynamic traffic assignment model. Transp Res Rec (1493):199–206

  27. Javani B, Babazadeh A (2017) Origin-destination-based truncated quadratic programming algorithm for traffic assignment problem. Transportation Letters 9(3):166–176

    Article  Google Scholar 

  28. Javani B, Babazadeh A, Ceder A (2019) Path-based capacity-restrained dynamic traffic assignment algorithm. Transportmetrica B: Transp Dyn 7(1):741-764

  29. Jayakrishnan R, Mahmassani HS, Hu TY (1994) An evaluation tool for advanced traffic information and management systems in urban networks. Transp Res C 2(3):129–147

    Article  Google Scholar 

  30. Jin WL (2015) Point queue models: a unified approach. Transp Res B Methodol 77:1–16

    Article  Google Scholar 

  31. Kachroo P, Shlayan N (2013) Dynamic traffic assignment: a survey of mathematical models and techniques. In: Advances in dynamic network modeling in complex transportation systems. Springer, New York, pp 1–25

    Google Scholar 

  32. Larsson T, Patriksson M (1995) An augmented Lagrangean dual algorithm for link capacity side constrained traffic assignment problems. Transp Res B Methodol 29(6):433–455

    Article  Google Scholar 

  33. Lo HK, Szeto WY (2002a) A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transp Res B Methodol 36(5):421–443

    Article  Google Scholar 

  34. Lo HK, Szeto WY (2002b) A cell-based dynamic traffic assignment model: formulation and properties. Math Comput Model 35(7):849–865

    Article  Google Scholar 

  35. Mahut M, Florian M (2010) Traffic simulation with dynameq. In: Fundamentals of traffic simulation. Springer, New York, pp 323–361

    Google Scholar 

  36. Mahut M, Florian M, Tremblay N, Campbell M, Patman D, McDaniel Z (2004) Calibration and application of a simulation-based dynamic traffic assignment model. Transp Res Rec 1876:101–111

    Article  Google Scholar 

  37. Merchant DK, Nemhauser GL (1978a) A model and an algorithm for the dynamic traffic assignment problems. Transp Sci 12(3):183–199

    Article  Google Scholar 

  38. Merchant DK, Nemhauser GL (1978b) Optimality conditions for a dynamic traffic assignment model. Transp Sci 12(3):200–207

    Article  Google Scholar 

  39. Mun JS (2007) Traffic performance models for dynamic traffic assignment: an assessment of existing models. Transp Rev 27(2):231–249

    Article  Google Scholar 

  40. Nie YM (2011) A cell-based Merchant–Nemhauser model for the system optimum dynamic traffic assignment problem. Transp Res B Methodol 45(2):329–342

    Article  Google Scholar 

  41. Nie X, Zhang HM (2005a) A comparative study of some macroscopic link models used in dynamic traffic assignment. Netw Spat Econ 5(1):89–115

    Article  Google Scholar 

  42. Nie X, Zhang HM (2005b) Delay-function-based link models: their properties and computational issues. Transp Res B Methodol 39(8):729–751

    Article  Google Scholar 

  43. Nie YM, Zhang HM (2010) Solving the dynamic user optimal assignment problem considering queue spillback. Netw Spat Econ 10(1):49–71

    Article  Google Scholar 

  44. Nie Y, Zhang HM, Lee DH (2004) Models and algorithms for the traffic assignment problem with link capacity constraints. Transp Res B Methodol 38(4):285–312

    Article  Google Scholar 

  45. Nie YM, Ma J, Zhang HM (2008) A polymorphic dynamic network loading model. Comput Aided Civ Inf Eng 23(2):86–103

    Article  Google Scholar 

  46. Papageorgiou M, Ben-Akiva M, Bottom J, Bovy PH, Hoogendoorn SP, Hounsell NB, Kotsialos A, McDonald M (2007) ITS and traffic management. Handbooks in operations research and management science, 14, p 715–774

  47. Peeta S, Mahmassani HS (1995) System optimal and user equilibrium time-dependent traffic assignment in congested networks. Ann Oper Res 60(1):81–113

    Article  Google Scholar 

  48. Ran B, Boyce DE, LeBlanc LJ (1993) A new class of instantaneous dynamic user-optimal traffic assignment models. Oper Res 41(1):192–202

    Article  Google Scholar 

  49. Shahbandi MG, Babazadeh A (2019) Analysis of a joint entry-and distance-based cordon pricing scheme: a dynamic modeling approach. J Mod Transp 27(1):25–38

  50. Shahpar AH, Aashtiani HZ, Babazadeh A (2008) Dynamic penalty function method for the side constrained traffic assignment problem. Appl Math Comput 206(1):332–345

    Google Scholar 

  51. Sheffi Y (1985) Urban transportation networks. Prentice-Hall, Englewood Cliffs, N.J

    Google Scholar 

  52. Szeto WY (2013) Cell-based dynamic equilibrium models. In: Advances in dynamic network modeling in complex transportation systems. Springer, New York, pp 163–192

    Google Scholar 

  53. Szeto WY, Wong SC (2012) Dynamic traffic assignment: model classifications and recent advances in travel choice principles. Cent Eur J Eng 2(1):1–18

  54. Ukkusuri SV, Han L, Doan K (2012) Dynamic user equilibrium with a path based cell transmission model for general traffic networks. Transp Res B Methodol 46(10):1657–1684

    Article  Google Scholar 

  55. Wardrop J (1952) Road paper. Some theoretical aspects of road traffic research. ICE Proc: Eng Div 1(3):325–362

  56. Zhang HM, Nie Y, Qian Z (2013) Modelling network flow with and without link interactions: the cases of point queue, spatial queue and cell transmission model. Transportmetrica B: Transp Dyn 1(1):33–51

  57. Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transp Sci 34(1):37–49

    Article  Google Scholar 

  58. Ziliaskopoulos AK, Waller ST, Li Y, Byram M (2004) Large-scale dynamic traffic assignment: implementation issues and computational analysis. J Transp Eng 130(5):585–593

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the three anonymous reviewers for their thoughtful comments and constructive suggestions.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Abbas Babazadeh.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Javani, B., Babazadeh, A. Path-Based Dynamic User Equilibrium Model with Applications to Strategic Transportation Planning. Netw Spat Econ 20, 329–366 (2020). https://doi.org/10.1007/s11067-019-09479-0

Download citation

Keywords

  • Analytical model
  • Dynamic traffic assignment
  • Path-based algorithm
  • Advanced traveler information systems
  • Dynamic traffic demand management
  • Large scale network