Abstract
The Origin-Destination (OD) travel demand is an essential component of transportation analysis, particularly for simulation models, such as static or dynamic traffic assignment that assess the impact of various strategic transportation plans. The conventional formulation of the OD estimation from traffic measurements is a bi-level optimization problem with equilibrium constraints. However, tackling bi-level problems for large-scale networks is computationally challenging, preventing the scalability of OD estimation. This paper presents a single-level join formulation of the travel demand estimation problem under Stochastic User Equilibrium (SUE) as a non-linear equation system. This single level formulation uses an extension of the SUE assignment fixed point formulation, making it transparent to the congestion and route choice model. A Jacobian free version of the Gauss-Newton algorithm is used to solve the model, which gave the freedom to incorporate multiple sources of traffic measurements in the estimation process. Numerical results on two networks illustrate the effectiveness and efficiency of the proposed methodology. In addition, estimation results indicate that the new formulation is robust with respect to count location coverage, measurement errors, and historical OD demand.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the economics of transportation. Technical report (1956)
Cantarella, G.E.: A general fixed-point approach to multimode multi-user equilibrium assignment with elastic demand. Transp. Sci. 31(2), 107–128 (1997). https://EconPapers.repec.org/RePEc:inm:ortrsc:v:31:y:1997:i:2:p:107-128
Cascetta, E.: Estimation of trip matrices from traffic counts and survey data: a generalized least squares estimator. Transp. Res. Part B Methodol. 18(4–5), 289–299 (1984)
Fisk, C.: Game theory and transportation systems modelling. Transp. Res. Part B Methodol. 18(4–5), 301–313 (1984)
Gentile, G., Velon’a, P., Cantarella, G.E.: Uniqueness of stochastic user equilibrium with asymmetric volume-delay functions for merging and diversion. EURO J. Transp. Logist. 3(3), 309–331 (2014)
LeBlanc, L.J., Farhangian, K.: Selection of a trip table which reproduces observed link flows. Transp. Res. Part B Methodol. 16(2), 83–88 (1982)
Ma, W., Qian, Z.: A generalized single-level formulation for origin–destination estimation under stochastic user equilibrium. Transp. Res. Rec. 2672(48), 58–68 (2018)
Maher, M.J.: Inferences on trip matrices from observations on link volumes: a bayesian statistical approach. Transp. Res. Part B Methodol. 17(6), 435–447 (1983)
Maher, M.J., Zhang, X., Van Vliet, D.: A bi-level programming approach for trip matrix estimation and traffic control problems with stochastic user equilibrium link flows. Transp. Res. Part B Methodol. 35(1), 23–40 (2001)
Marzano, V., Papola, A., Simonelli, F.: Limits and perspectives of effective o–d matrix correction using traffic counts. Transp. Res. Part C Emerg. Technol. 17(2), 120–132 (2009)
Meng, Q., Yang, H., Bell, M.G.: An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem. Transp. Res. Part B Methodol. 35(1), 83–105 (2001)
Nakayama, S., Kitamura, R., Fujii, S.: Drivers’ route choice rules and network behavior: do drivers become rational and homogeneous through learning? Transp. Res. Rec. 1752(1), 62–68 (2001)
Nguyen, S.: Estimating and OD Matrix from Network Data: a Network Equilibrium Approach. Universit’e de Montr’eal, Centre de recherche sur les transports (1977)
Nie, Y., Zhang, H.M., Recker, W.: Inferring origin–destination trip matrices with a decoupled gls path flow estimator. Transp. Res. Part B Methodol. 39(6), 497–518 (2005)
Nie, Y.M., Zhang, H.M.: A relaxation approach for estimating origin–destination trip tables. Netw. Spat. Econ. 10(1), 147–172 (2010)
Robillard, P.: Estimating the od matrix from observed link volumes. Transp. Res. 9(2–3), 123–128 (1975)
Sheffi, Y.: Urban Transportation Networks, vol. 6. Prentice-Hall, Englewood Cliffs, NJ (1985)
Shen, W., Wynter, L.: A new one-level convex optimization approach for estimating origin–destination demand. Transp. Res. Part B Methodol. 46(10), 1535–1555 (2012)
Wang, Y., et al.: A two-stage algorithm for origin-destination matrices estimation considering dynamic dispersion parameter for route choice. PLoS ONE 11(1), e0146850 (2016)
Yang, H.: Heuristic algorithms for the bilevel origin-destination matrix estimation problem. Transp. Res. Part B Methodol. 29(4), 231–242 (1995)
Yang, H., Meng, Q., Bell, M.G.: Simultaneous estimation of the origin-destination matrices and travel-cost coefficient for congested networks in a stochastic user equilibrium. Transp. Sci. 35(2), 107–123 (2001)
Yang, H., Sasaki, T., Iida, Y., Asakura, Y.: Estimation of origin-destination matrices from link traffic counts on congested networks. Transp. Res. Part B Methodol. 26(6), 417–434 (1992)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Eldafrawi, M., Gentile, G. (2023). A Single-Level Joint Formulation for Travel Demand Estimation Under Stochastic User Equilibrium. In: Kabashkin, I., Yatskiv, I., Prentkovskis, O. (eds) Reliability and Statistics in Transportation and Communication. RelStat 2022. Lecture Notes in Networks and Systems, vol 640. Springer, Cham. https://doi.org/10.1007/978-3-031-26655-3_29
Download citation
DOI: https://doi.org/10.1007/978-3-031-26655-3_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-26654-6
Online ISBN: 978-3-031-26655-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)