Dynamic origin–destination demand flow estimation under congested traffic conditions Chung-Cheng Lu a , Xuesong Zhou b,⇑ , Kuilin Zhang c a Department of Transportation and Logistics Management, National Chiao Tung University, Hsinchu 30050, Taiwan b Department of Civil and Environmental Engineering, University of Utah, Salt Lake City, UT 84112, USA c Transportation Research and Analysis Computing Center, Energy Systems Division, Argonne National Laboratory, Argonne, IL 60439, USA article info Article history: Received 22 July 2012 Received in revised form 10 May 2013 Accepted 13 May 2013 Keywords: OD demand estimation Path flow estimator Lagrangian relaxation Newell’s simplified kinematic wave theory abstract This paper presents a single-level nonlinear optimization model to estimate dynamic ori- gin–destination (OD) demand. The model is a path flow-based optimization model, which incorporates heterogeneous sources of traffic measurements and does not require explicit dynamic link-path incidences. The objective is to minimize (i) the deviation between observed and estimated traffic states and (ii) the deviation between aggregated path flows and target OD flows, subject to the dynamic user equilibrium (DUE) constraint represented by a gap-function-based reformulation. A Lagrangian relaxation-based algorithm which dualizes the difficult DUE constraint to the objective function is proposed to solve the model. This algorithm integrates a gradient-projection-based path flow adjustment method within a column generation-based framework. Additionally, a dynamic network loading (DNL) model, based on Newell’s simplified kinematic wave theory, is employed in the DUE assignment process to realistically capture congestion phenomena and shock wave propagation. This research also derives analytical gradient formulas for the changes in link flow and density due to the unit change of time-dependent path inflow in a general network under congestion conditions. Numerical experiments conducted on three different networks illustrate the effectiveness and shed some light on the properties of the proposed OD demand estimation method. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Time-dependent origin–destination (OD) demand matrices are fundamental inputs for dynamic traffic assignment (DTA) models to describe network flow evolution as a result of interactions of individual travelers. Moreover, many emerging intel- ligent traffic management applications call for reliable estimates of dynamic OD demand, in order to generate proactive, coordinated traffic information provision and flow control strategies based on reliable traffic state estimates. Transportation authorities and practitioners have long been concerned about the unavailability of high quality time-dependent OD demand estimates which limits the potential for DTA deployments to analyze and alleviate traffic congestion. In the past decades, a rich body of literature, to be presented as follows, has been devoted to the methods of estimating static or time-dependent OD demand tables. However, the development of theoretically sound and practically deployable approaches for time-depen- dent OD demand estimation, particularly under congested conditions, remains a critical and challenging problem that is attracting significant attention from transportation researchers. 0968-090X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trc.2013.05.006 ⇑ Corresponding author. Tel.: +1 801 585 6590; fax: +1 801 585 5477. E-mail addresses: jasoncclu@gmail.com (C.-C. Lu), zhou@eng.utah.edu (X. Zhou), kzhang@anl.gov (K. Zhang). Transportation Research Part C 34 (2013) 16–37 Contents lists available at SciVerse ScienceDirect Transportation Research Part C journal homepage: www.elsevier.com/locate/trc