Sensitivity-Based Linear Approximation Method to Estimate Time-Dependent Origin–Destination Demand in Congested Networks

This paper presents a bi-level optimization problem to estimate offline time-dependent origin–destination (time-dependent O-D) demand on the basis of link flows and historical O-D matrices. The upper-level problem aimed to minimize the summation of errors in both traffic counts and O-D demand. Conventionally, O-D flows are linearly mapped to link flows with the assignment matrix proportions obtained from the dynamic traffic assignment, which is typically formulated as the lower-level problem. However, the linear relationship may be invalid when congestion builds up in the network, and a nonlinear relation between O-D flows and link flows may result. The nonlinearity may lead to a converged solution that is far from the global optimum. An accurate solution should be able to relax the linear assumption and to consider the effect of other O-D flows on the links’ traffic volumes. In this study, a solution method that relied on the sensitivity of assignment proportions to O-D flows was proposed and applied; it required a number of further assignments. To overcome the extra computational requirement, a heuristic method to exclude the extra assignments and to improve the performance of the solution was proposed. The proposed algorithm was applied to multiple networks of varying sizes and congestion levels. The results demonstrated the efficiency of the proposed method for congested networks with less computation time.