Networks and Spatial Economics

, Volume 19, Issue 4, pp 1123–1142 | Cite as

Subnetwork Origin-Destination Matrix Estimation Under Travel Demand Constraints

  • Chao Sun
  • Yulin Chang
  • Yuji ShiEmail author
  • Lin Cheng
  • Jie Ma


This paper proposes a subnetwork origin-destination (OD) matrix estimation model under travel demand constraints (SME-DC) that explicitly considers both internal-external subnetwork connections and OD demand consistency between the subnetwork and full network. This new model uses the maximum entropy of OD demands as the objective function and uses the total traffic generations (attractions) along with some fixed OD demands of the subnetwork OD nodes as the constraints. The total traffic generations and attractions along with the fixed OD demands of the subnetwork OD nodes are obtained through an OD node transformation and subnetwork topology analysis. For solving the proposed model, a convex combination method is used to convert the nonlinear SME-DC to the classical linear transportation problem, and a tabular method is used to solve the transportation problem. The Sioux Falls network and Kunshan network were provided to illustrate the essential ideas of the proposed model and the applicability of the proposed solution algorithm.


Subnetwork topology analysis Origin-destination matrix estimation Travel demand constraints Convex combination method Tabular method 



The authors are grateful to two anonymous referees for their constructive comments and suggestions to improve the quality and clarity of the paper. This research is supported by the National Natural Science Foundation of China (No. 71801115) and the Key Research and Development Projects of Zhenjiang City.


  1. Bar-Gera H, Boyce SD, Nie YM (2012) User-equilibrium route flows and the condition of proportionality. Transp Res B Methodol 46(3):440–462CrossRefGoogle Scholar
  2. Bazaraa MS, Sherali HD, Shetty CM (2013) Nonlinear programming: theory and algorithms, 3rd edn. Wiley, HobokenGoogle Scholar
  3. Bekhor S, Toledo T, Prashker JN (2008) Effects of choice set size and route choice models on path-based traffic assignment. Transportmetrica 4(2):117–133CrossRefGoogle Scholar
  4. Bell MGH (1983) The estimation of an origin-destination matrix from traffic counts. Transp Sci 17(2):198–217CrossRefGoogle Scholar
  5. Bell MGH (1991) The estimation of origin-destination matrices by constrained generalised least squares. Transp Res B Methodol 25(1):13–22CrossRefGoogle Scholar
  6. Boyles SD (2012) Bush-based sensitivity analysis for approximating subnetwork diversion. Transp Res B Methodol 46(1):139–155CrossRefGoogle Scholar
  7. Bruton MJ (1975) Introduction to transportation planning. Hutchinson, LondonGoogle Scholar
  8. Chen A, Kasikitwiwat P, Yang C (2013) Alternate capacity reliability measures for transportation networks. J Adv Transp 47(1):79–104CrossRefGoogle Scholar
  9. De Grange L, Fernández E, de Cea J (2010) A consolidated model of trip distribution. Transport Res E-Log 46(1):61–75CrossRefGoogle Scholar
  10. Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271CrossRefGoogle Scholar
  11. Facchinei F, Pang JS (2007) Finite-dimensional variational inequalities and complementarity problems. Springer Science & Business Media, BerlinGoogle Scholar
  12. Fisk CS (1988) On combining maximum entropy trip matrix estimation with user optimal assignment. Transp Res B Methodol 22(1):69–73CrossRefGoogle Scholar
  13. Frank M, Wolfe P (1956) An algorithm for quadratic programming. Nav Res Logist 3(1–2):95–110CrossRefGoogle Scholar
  14. Ge Q, Fukuda D (2016) Updating origin-destination matrices with aggregated data of GPS traces. Transp Res C Emerg Technol 69:291–312CrossRefGoogle Scholar
  15. Gemar M, Bringardner J, Boyles S, Machemehl R (2014) Subnetwork analysis for dynamic traffic assignment models: strategy for estimating demand at subnetwork boundaries. Transp Res Rec 2466:153–161CrossRefGoogle Scholar
  16. Grange L, González F, Bekhor S (2016) Path flow and trip matrix estimation using link flow density. Netw Spat Econ 2017, 17(1): 173-195CrossRefGoogle Scholar
  17. Haghani AE, Daskin MS (1983) Network design application of an extraction algorithm for network aggregation. Transp Res Rec 944: 37-46Google Scholar
  18. Hendrickson C, McNeil S (1984) Matrix entry estimation errors. Proceedings of the 9th International Symposium on Transportation and Traffic Theory. Delft University The Netherlands, p 413–430Google Scholar
  19. Iqbal MS, Choudhury CF, Wang P, González MC (2014) Development of origin-destination matrices using mobile phone call data. Transp Res C Emerg Technol 40:63–74CrossRefGoogle Scholar
  20. Jafari E, Boyles SD (2016) Improved bush-based methods for network contraction. Transp Res B Methodol 83:298–313CrossRefGoogle Scholar
  21. Kuwahara M, Sullivan EC (1987) Estimating origin-destination matrices from roadside survey data. Transp Res B Methodol 21(3):233–248CrossRefGoogle Scholar
  22. Leblanc LJ (1973) Mathematical programming algorithms for large-scale network equilibrium and network design problems. Unpublished PhD dissertation, Northwestern University, EvanstonGoogle Scholar
  23. Li T (2015) A bi-level model to estimate the us air travel demand. Asia Pac J Oper Res 32(02):1–34CrossRefGoogle Scholar
  24. Li T, Wu J, Sun H, Gao Z (2015) Integrated co-evolution model of land use and traffic network design. Netw Spat Econ 2016, 16(2): 579-603CrossRefGoogle Scholar
  25. Maher MJ (1983) Inferences on trip matrices from observations on link volumes: a Bayesian statistical approach. Transp Res B Methodol 17(6):435–447CrossRefGoogle Scholar
  26. Millard-Ball A (2015) Phantom trips: overestimating the traffic impacts of new development. J Transp Land Use 8(1):31–49CrossRefGoogle Scholar
  27. Mishra S, Wang Y, Zhu X, Moeckel R, Mahapatra S (2013) Comparison between gravity and destination choice models for trip distribution in Maryland. In: Transportation Research Board 92nd Annual MeetingGoogle Scholar
  28. Moya-Gómez B, Salas-Olmedo MH, García-Palomares JC, Gutiérrez J (2018) Dynamic accessibility using big data: the role of the changing conditions of network congestion and destination attractiveness. Netw Spat Econ 18(2):273–290CrossRefGoogle Scholar
  29. Nihan NL, Davis GA (1987) Recursive estimation of origin-destination matrices from input/output counts. Transp Res B Methodol 21(2):149–163CrossRefGoogle Scholar
  30. Rossi TF, McNeil S, Hendrickson C (1989) Entropy model for consistent impact-fee assessment. J Urban Plan Dev 115(2):51–63CrossRefGoogle Scholar
  31. Ruiter E (1967) Towards a better understanding of the intervening opportunities model. Transp Res 1:47–56CrossRefGoogle Scholar
  32. Sherali HD, Sivanandan R, Hobeika AG (1994) A linear programming approach for synthesizing origin-destination trip tables from link traffic volumes. Transp Res B Methodol 28(3):213–233CrossRefGoogle Scholar
  33. Szeto WY, Jiang Y, Wang DZW, Sumalee A (2015) A sustainable road network design problem with land use transportation interaction over time. Netw Spat Econ 15(3):791–822CrossRefGoogle Scholar
  34. Toole JL, Colak S, Sturt B, Alexander LP, Evsukoff A, González MC (2015) The path most traveled: travel demand estimation using big data resources. Transp Res C Emerg Technol 58:162–177CrossRefGoogle Scholar
  35. Wei C, Asakura Y (2013) A Bayesian approach to traffic estimation in stochastic user equilibrium networks. Transp Res C Emerg Technol 36:446–459CrossRefGoogle Scholar
  36. Winston WL, Goldberg JB (2004) Operations research: applications and algorithms. Duxbury press, BelmontGoogle Scholar
  37. Xie C, Duthie J (2015) An excess-demand dynamic traffic assignment approach for inferring origin-destination trip matrices. Netw Spat Econ 15(4):947–979CrossRefGoogle Scholar
  38. Xie C, Kockelman KM, Waller ST (2010) Maximum entropy method for subnetwork origin-destination trip matrix estimation. Transp Res Rec 2196:111–119CrossRefGoogle Scholar
  39. Xie C, Kockelman KM, Waller ST (2011) A maximum entropy-least squares estimator for elastic origin-destination trip matrix estimation. Transp Res B Methodol 45(9):1465–1482CrossRefGoogle Scholar
  40. Yang H, Zhou J (1998) Optimal traffic counting locations for origin-destination matrix estimation. Transp Res B Methodol 32(2):109–126CrossRefGoogle Scholar
  41. Yang H, Sasaki T, Iida Y, Asakura Y (1992) Estimation of origin-destination matrices from link traffic counts on congested networks. Transp Res B Methodol 26(6):417–434CrossRefGoogle Scholar
  42. Yang H, Bell MGH, Meng Q (2000) Modeling the capacity and level of service of urban transportation networks. Transp Res B Methodol 34(4):255–275CrossRefGoogle Scholar
  43. Zhou X, Erdogan S, Mahmassani H (2006) Dynamic origin-destination trip demand estimation for subarea analysis. Transp Res Rec 1964:176–184CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Chao Sun
    • 1
    • 2
  • Yulin Chang
    • 1
    • 3
  • Yuji Shi
    • 1
    Email author
  • Lin Cheng
    • 2
  • Jie Ma
    • 2
  1. 1.School of Automotive and Traffic EngineeringJiangsu UniversityZhenjiangChina
  2. 2.School of TransportationSoutheast UniversityNanjingChina
  3. 3.Faculty of Engineering and EnvironmentUniversity of SouthamptonSouthamptonUK

Personalised recommendations