Origin-Destination Matrix Estimation Using Socio-Economic Information and Traffic Counts on Uncongested Networks

Document Type : Research Paper


1 Ph.D., Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

2 Associate Professor, Department of Transportation Engineering, Isfahan University of Technology, Isfahan, Iran

3 MSc. Department of Industrial and System Engineering, Isfahan University of Technology, Isfahan, Iran


The travel demand matrix, also known as an origin-destination matrix (OD matrix), is essential in transportation planning. Given their nature and extent of operation, direct methods of estimating the matrix often impose unusually high costs in terms of both time and human resources. Thus, over the past three decades, numerous attempts have been made to propose indirect methods of estimating and updating the OD matrix. Using traffic counts to estimate the OD matrix is one of those indirect methods. However, because there are insufficient of traffic counts, indirect methods mostly lead to multiple OD matrices. One way to overcome this drawback is to use a previously estimated matrix from available data (called the old matrix) for new matrix estimation. Since uncongested networks rarely suffer from congestion, they have not been at the center of attention by researchers and transportation planners; thus, no old OD matrix is available for these networks. This study proposes a two-stage approach for estimating the OD matrix on uncongested networks. Firstly, an initial OD matrix is built using a travel distribution model (e.g., gravity model) together with local socio-economic information and available traffic counts across the network. Secondly, by considering budget constraints and using Bayesian inference, the optimum counting sensor locations are determined and by applying the collected information and the precision of the initial OD matrix is improved. To evaluate the proposed solution, the algorithm is then applied to the Sioux Falls network. The results prove the efficiency and precision of the approach.


- Abrahamsson, T. (1998) "Estimation of origin-destination matrices using traffic counts-a literature survey".
- Antoniou, C., Barceló, J., Breen, M., Bullejos, M., Casas, J., Cipriani, E., ... & Montero, L. (2016) "Towards a generic benchmarking platform for origin–destination flows estimation/updating algorithms: Design, demonstration and validation", Transportation Research Part C: Emerging Technologies, No. 66, pp. 79-98. https://doi.org/10.1016/j.trc.2015.08.009
- Bao, X., Li, H., Qin, L., Xu, D., Ran, B., & Rong, J. (2016) "Sensor location problem optimization for traffic network with different spatial distributions of traffic information", Sensors, Vol. 16, No. 11, pp. 1790. https://doi.org/10.3390/s16111790
- Bauer, D., Richter, G., Asamer, J., Heilmann, B., Lenz, G. and Kölbl, R. (2018) "Quasi-Dynamic Estimation of OD Flows From Traffic Counts Without Prior OD Matrix", IEEE Transactions on Intelligent Transportation Systems, Vol. 19, No. 6, pp. 2025-2034.  https://doi.org/10.1109/TITS.2017.2741528
- Bera, S. and Rao, K.V. (2011) "Estimation of origin-destination matrix from traffic counts: the state of the art".
- Berman, O., Bertsimas, D. and Larson, R.C. (1995) "Locating discretionary service facilities, II: maximizing market size, minimizing inconvenience", Operations Research, Vol. 43, No. 4, pp. 623-63. https://doi.org/10.1287/opre.43.4.623
- Castillo, E., Gallego, I., Menéndez, J.M. and Rivas, A. (2010) "Optimal use of plate-scanning resources for route flow estimation in traffic networks", IEEE Transactions on Intelligent Transportation Systems, Vol. 11, No. 2, pp. 380-391. https://doi.org/10.1109/TITS.2010.2042958
- Castillo, E., Menéndez, J.M. and Jiménez, P. (2008) "Trip matrix and path flow reconstruction and estimation based on plate scanning and link observations", Transportation Research Part B: Methodological, Vol. 42, No. 5, pp. 455-481. https://doi.org/10.1016/j.trb.2007.09.004
- Cools, M., Moons, E. and Wets, G. (2010) "Assessing the quality of origin-destination matrices derived from activity travel surveys: Results from a Monte Carlo experiment", Transportation Research Record: Journal of the Transportation Research Board, No. 2183, pp. 49-59. https://doi.org/10.3141/2183-06
- De Grange, L., González, F. and Bekhor, S. (2017) "Path flow and trip matrix estimation using link flow density. Networks and Spatial Economics", Vol. 17, No. 1, pp. 173-195. https://doi.org/10.1007/s11067-016-9322-1
- Doblas, J. and Benitez, F.G. (2005) "An approach to estimating and updating origin–destination matrices based upon traffic counts preserving the prior structure of a survey matrix", Transportation Research Part B: Methodological, Vol. 39, No. 7, pp. 565-591. https://doi.org/10.1016/j.trb.2004.06.006
- Elyasi, M., Faezi, S. F., Haghsheno-Sabet, M., & Mazaheri, M. (2018) "An ANP-based Model for Location of Fixed Speed Cameras", International Journal of Transportation Engineering, Vol. 6, No. 1, pp. 17-34. https://dx.doi.org/10.22119/ijte.2017.52975
- Ge, Q., & Fukuda, D. (2016) "Updating origin–destination matrices with aggregated data of GPS traces", Transportation Research Part C: Emerging Technologies, No. 69, pp. 291-312. https://doi.org/10.1016/j.trc.2016.06.002
- Gentili, M. and Mirchandani, P. (2011) "Survey of models to locate sensors to estimate traffic flows", Transportation Research Record: Journal of the Transportation Research Board, No. 2243, pp. 108-116. https://doi.org/10.3141/2243-13
- Hadavi, M., & Shafahi, Y. (2016) "Vehicle identification sensor models for origin–destination estimation", Transportation Research Part B: Methodological, No. 89, pp. 82-106. https://doi.org/10.1016/j.trb.2016.03.011
-  Hafezi, Mohammad Hesam, et al. "A Novel Method for Travel System Patterns." International Journal of Transportation Engineering 1.2 (2013): 93-100. https://dx.doi.org/10.22119/ijte.2013.3235
- Hodgson, M. J. (1990) "A Flow‐capturing location‐allocation model", Geographical Analysis, Vol. 22, No. 3, pp. 270-279. https://doi.org/10.1111/j.1538-4632.1990.tb00210.x
- Hong, I. and Jung, W.S. (2016) "Application of gravity model on the Korean urban bus network", Physica A: Statistical Mechanics and its Applications, No. 462, pp. 48-55. https://doi.org/10.1016/j.physa.2016.06.055
- Kanafany, A. (1983). Transportation Demand Analysis. New York, NY: Mc Graw-Hil
- Karimi, H., Ebrahimi, A., Shetab Bousshehri, S. (2017) "Optimum Counting Location to update Origin-Destination Matrix Using Bayesian inference (Case Study: City of Isfahan) ", Quarterly Journal of Transportation Engineering, Vol. 8, No. 3, pp. 451-471, In Persian.
- Kim, H., Nam, D., Suh, W. and Cheon, S.H. (2018) "Origin-destination trip table estimation based on subarea network OD flow and vehicle trajectory data", Transportation Planning and Technology, Vol. 41, No. 3, pp. 265-285. https://doi.org/10.1080/03081060.2018.1435437
- Lam, W.H.K. and Lo, H.P. (1990) "Accuracy of OD estimates from traffic counts", Traffic engineering & control, Vol. 31, No. 6.
- Larsson, T., Lundgren, J.T. and Peterson, A. (2010) "Allocation of Link Flow Detectors for Origin‐Destination Matrix Estimation—A Comparative Study", Computer‐Aided Civil and Infrastructure Engineering, Vol. 52, No. 2, pp. 116-131. https://doi.org/10.1111/j.1467-8667.2009.00625.x
- Leblanc, L.J. (1975) "An algorithm for the discrete network design problem", Transportation Science, Vol. 9, No. 3, pp. 183-199. https://doi.org/10.1287/trsc.9.3.183
- Michau, G., Pustelnik, N., Borgnat, P., Abry, P., Nantes, A., Bhaskar, A., & Chung, E. (2017) "A primal-dual algorithm for link dependent origin destination matrix estimation", IEEE Transactions on Signal and Information Processing over Networks, Vol. 3, No. 1, pp. 104-113. https://doi.org/10.1109/TSIPN.2016.2623094
- Ortúzar, J., & Willumsen, L. G. (2011). Trip distribution modelling. Modelling transport (4th ed., pp. 175–206).
- Perrakis, K., Karlis, D., Cools, M. and Janssens, D. (2015) "Bayesian inference for transportation origin–destination matrices: the Poisson–inverse Gaussian and other Poisson mixtures", Journal of the Royal Statistical Society: Series A (Statistics in Society), Vol. 178, No. 1, pp. 271-296. https://doi.org/10.1111/rssa.12057
- Ryu, S., Chen, A., Zhang, H.M. and Recker, W. (2014) "Path flow estimator for planning applications in small communities", Transportation Research Part A: Policy and Practice, No. 69, pp. 212-242. https://doi.org/10.1016/j.tra.2014.08.019
- Stopher, P.R. and Greaves, S.P. (2007) "Household travel surveys: Where are we going? ", Transportation Research Part A: Policy and Practice, Vol. 41, No. 5, pp. 367-381. https://doi.org/10.1016/j.tra.2006.09.005
- Tang, S. and Zhang, H. (2013) "Primal-dual heuristic for path flow estimation in medium to large networks", Transportation Research Record: Journal of the Transportation Research Board, No. 2333, pp. 91-99. https://doi.org/10.3141/2333-11
- Viti, F., Rinaldi, M., Corman, F. and Tampère, C.M. (2014) "Assessing partial observability in network sensor location problems", Transportation research part B: methodological, Vol. 70, pp. 65-89. https://doi.org/10.1016/j.trb.2014.08.002
- Wei, C. and Asakura, Y. (2013) "A Bayesian approach to traffic estimation in stochastic user equilibrium etworks", Transportation Research Part C: Emerging Technologies, No. 36, pp. 446-459. https://doi.org/10.1016/j.sbspro.2013.05.032
- Wilson, A. G. (1967) "A statistical theory of spatial distribution models", Transportation research, Vol. 1, No. 3, pp. 253-269.
- Xie, C., Kockelman, K.M. and Waller, S.T. (2011) "A maximum entropy-least squares estimator for elastic origin–destination trip matrix estimation", Transportation Research Part B: Methodological, Vol. 45, No. 9, pp. 1465-1482. https://doi.org/10.1016/j.sbspro.2011.04.514
- Yang, H., Iida, Y. and Sasaki, T. (1991) "An analysis of the reliability of an origin-destination trip matrix estimated from traffic counts", Transportation Research Part B: Methodological, Vol. 25, No. 5, pp. 351-363. https://doi.org/10.1016/0191-2615(91)90028-H
- Yang, H. and Zhou, J. (1998) "Optimal traffic counting locations for origin–destination matrix estimation", Transportation Research Part B: Methodological, Vol. 32, No. 2, pp. 109-126. https://doi.org/10.1016/S0191-2615(97)00016-7
- Ye, P., & Wen, D. (2017) "Optimal traffic sensor location for origin–destination estimation using a compressed sensing framework", IEEE Transactions on Intelligent Transportation Systems, Vol. 18, No. 7, pp. 1857-1866. https://doi.org/10.1109/TITS.2016.2614828
- Yim, P.K. and Lam, W.H. (1998) "Evaluation of count location selection methods for estimation of OD matrices", Journal of transportation engineering, Vol. 124, No. 4, pp. 376-383. https://doi.org/10.1061/(ASCE)0733-947X(1998)124:4(376)