Stochastic programming approach for static origin–destination matrix reconstruction problem

We propose a stochastic programming approach for a static origin–destination (OD) reconstruction problem. We focus on the reconstruction of route flows such that the likelihood function of route flows is maximized. The route volumes are assumed to follow exponential families that are known or estimated in advance. The consideration of the joint distribution function of route flows eliminates the route selection from the model, as the route choice patterns are embedded in the distribution of the route flows. We assume that additional information regarding the traffic counts (i.e., node counts, link counts, and turn counts) is available. Finally, solution methodologies for different stochastic programmings are proposed: barrier method and Primal-dual interior point method for Quadratic Programming and Convex Programming respectively. We compared the proposed stochastic models with the entropy approach. Experimental results indicate that the inclusion of traffic-count information in the stochastic model significantly improves the accuracy of OD reconstruction if we can predict the correct distribution of route flows. Meanwhile the entropy approach requires the inclusion of the additional information on the true volumes of route flows to achieve a similar level of performance. We apply the proposed algorithm to the bus transit system of Seoul, Korea using bus-card data. Compared with the real OD volumes, the reconstruction is fairly accurate.