Estimation of origin–destination matrices using link counts and partial path data

  • Mojtaba Rostami NasabEmail author
  • Yousef Shafahi


After several decades of work by several talented researchers, estimation of the origin–destination matrix using traffic data has remained very challenging. This paper presents a set of innovative methods for estimation of the origin–destination matrix of large-scale networks, using vehicle counts on links, partial path data obtained from an automated vehicle identification system, and combinations of both data. These innovative methods are used to solve three origin–destination matrix estimation models. The first model is an extension of Spiess’s model which uses vehicle count data while the second model is an extension of Jamali’s model and it uses partial path data. The third model is a multiobjective model which utilizes combinations of vehicle counts and partial path data. The methods were tested to estimate the origin–destination matrix of a large-scale network from Mashhad City with 163 traffic zones and 2093 links, and the results were compared with the conventional gradient-based algorithm. The results show that the innovative methods performed better as compared to the gradient-based algorithm.


Origin–destination matrix estimation Automated vehicle identification data Vehicle count data Innovative method Gradient-based algorithm 



The authors would like to thank PTV group for providing PTV VISUM software and anonymous reviewers who helped to improve the paper with their comments and suggestions.


  1. Asakura, Y., Hato, E., Kashiwadani, M.: Origin–destination matrices estimation model using automatic vehicle identification data and its application to the Han-Shin expressway network. Kluwer Acad. Publ. 27, 419–438 (2000)Google Scholar
  2. Ashok, K.: Estimation and prediction of time-dependent origin–destination flows. Ph.D. Thesis, Massachusetts Inst. Technol. USA. (1996).
  3. Baek, S., Lim, Y., Rhee, S., Choi, K.: Method for estimating population OD matrix based on probe vehicles. KSCE J. Civ. Eng. 14, 231–235 (2010). CrossRefGoogle Scholar
  4. Bera, S., Rao, K.V.K.: Estimation of origin-destination matrix from traffic counts: the state of the art. Eur. Transp. Trasp. Eur. 49, 3–23 (2011)Google Scholar
  5. Cantelmo, G., Cipriani, E., Gemma, A., Nigro, M.: An adaptive bi-level gradient procedure for the estimation of dynamic traffic demand. IEEE Trans. Intell. Transp. Syst. 15, 1348–1361 (2014). CrossRefGoogle Scholar
  6. Carrese, S., Cipriani, E., Mannini, L., Nigro, M.: Dynamic demand estimation and prediction for traffic urban networks adopting new data sources. Transp. Res. Part C Emerg. Technol. 81, 83–98 (2017). CrossRefGoogle Scholar
  7. Castillo, E., Menéndez, J.M., Jiménez, P.: Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations. Transp. Res. Part B Methodol. 42, 455–481 (2008). CrossRefGoogle Scholar
  8. Dixon, M.P., Rilett, L.R.: Population origin–destination estimation using automatic vehicle identification and volume data. J. Transp. Eng. 131, 75–82 (2005). CrossRefGoogle Scholar
  9. Doblas, J., Benitez, F.G.: An approach to estimating and updating origin-destination matrices based upon traffic counts preserving the prior structure of a survey matrix. Transp. Res. Part B Methodol. 39, 565–591 (2005). CrossRefGoogle Scholar
  10. Fu, C., Zhu, N., Ling, S., Ma, S., Huang, Y.: Heterogeneous sensor location model for path reconstruction. Transp. Res. Part B 91, 77–97 (2016). CrossRefGoogle Scholar
  11. Gentile, G.: Local user cost equilibrium: a bush-based algorithm for traffic assignment. Transp. A Transp. Sci. 10, 15–54 (2014). Google Scholar
  12. Gentile, G., Noekel, K.: Linear user cost equilibrium: a new algorithm for traffic assignment. In: European Transport Conference, At Leeuwenhorst Conference Centre, The Netherlands, pp. 1–52 (2009)Google Scholar
  13. Hadavi, M., Shafahi, Y.: Vehicle identification sensor models for origin–destination estimation. Transp. Res. Part B Methodol. 89, 82–106 (2016). CrossRefGoogle Scholar
  14. ITSR: Mashhad Comprehensive Transportation Studies. Sharif University of Technology, Tehran (1995)Google Scholar
  15. Jamali, A.: O–D demand estimation base on automatic vehicle identification data. Master Thesis, Sharif University Technology, Iran (2014)Google Scholar
  16. Kwon, J., Varaiya, P.: Real-time estimation of origin–destination matrices with partial trajectories from electronic toll collection tag data. Transp. Res. Rec. J. Transp. Res. Board. 1923, 119–126 (2005). CrossRefGoogle Scholar
  17. LeBlanc, L.J., Farhangian, K.: Selection of a trip table which reproduces observed link flows. Transp. Res. Part B 16, 83–88 (1982)CrossRefGoogle Scholar
  18. Nguyen, S.: Estimating an OD matrix from network data: a network equilibrium approach. Universite de Montreal, Centre de Recherche sur les Transports, Montreal (1977)Google Scholar
  19. Parry, K., Hazelton, M.L.: Estimation of origin–destination matrices from link counts and sporadic routing data. Transp. Res. Part B Methodol. 46, 175–188 (2012). CrossRefGoogle Scholar
  20. Sheffi, Y.: Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Inc., Englewood Cliffs (1985)Google Scholar
  21. Spiess, H.: A gradient approach for the O–D matrix adjustment problem. Centre for Research on Transportation, University of Montreal, Montreal (1990)Google Scholar
  22. Talebian Yazdi, P.: Solving location problem for vehicle identification sensors to observe or estimate path flows in large-scale networks. Master Thesis, Sharif University Technology, Iran (2018)Google Scholar
  23. Vasko, F.J., Lu, Y., Zyma, K.: What is the best greedy-like heuristic for the weighted set covering problem? Oper. Res. Lett. 44, 366–369 (2016). CrossRefGoogle Scholar
  24. Yang, X., Lu, Y., Hao, W.: Origin-destination estimation using probe vehicle trajectory and link counts. J. Adv. Transp. 18, 1–27 (2017). Google Scholar
  25. Zhou, X., Mahmassani, H.S.: Dynamic origin–destination demand estimation using automatic vehicle identification data. IEEE Trans. Intell. Transp. Syst. 7, 105–114 (2006). CrossRefGoogle Scholar
  26. Van Der Zijpp, N.: Dynamic origin–destination matrix estimation from traffic counts and automated vehicle identification data. Transp. Res. Rec. J. Transp. Res. Board. 1607, 87–94 (1997). CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Civil Engineering DepartmentSharif University of TechnologyTehranIran

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