Nonlinearity in time-dependent origin-destination demand estimation in congested networks

Time-dependent origin-destination (TDOD) demand estimation is often formulated as a bi-level quadratic optimization in which the estimated demand in the upper-level problem is evaluated iteratively through a dynamic traffic assignment (DTA) model in the lower level. When congestion forms and propagates in the network, traditional solutions assuming a linear relation between demand flow and link flow become inaccurate and yield biased solutions. In this study, we study a sensitivity-based method taking into account the impact of other OD flows on the links' traffic volumes and densities. Thereafter, we compare the performance of the proposed method with several well-established solution methods for TDOD demand estimation problem. The methods are applied to a benchmark study urban network and a major freeway corridor in Melbourne, Australia. We show that the incorporation of traffic density into flow-based models improves the accuracy of the estimated OD flows and assist solution algorithm in avoiding converging to a sub-optimal result. Moreover, the final results obtained from the proposed sensitivity-based method contains less amount of error while the method exceeds the problem's computational intensity compared to the traditional linear method.