Estimation of time-dependent origin–destination matrices for transit networks

In this paper, the estimation of time-dependent origin–destination (O–D) matrices for transit network based on observed passenger counts is given. The dynamic assignment framework is based on a schedule-based transit network model, which can help determine the time-dependent least cost paths between all O–D pairs, and for each of them the clock arrival times at the end nodes of all observed links (if any) in the transit network. An entropy-based approach is then employed to estimate the time-dependent O–D matrices based on the observed passenger counts at those observed links in the network. An efficient sparse algorithm is also proposed to solve the resulting mathematical programming problem. The estimation methodology is tested in a transit network from the Mass Transit Railway (MTR) system in Hong Kong, which is one of the busiest railway systems in the world. Both cases with and without prior information of the O–D matrices are considered for this network. The predicted matrices are then compared with the true matrices obtained from a sophisticated electronic fare collection system of MTR. Good agreement between predicted and observed matrices is found.