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Transportation networks are unprecedentedly complex with heterogeneousvehicular flow. Conventionally, vehicle classes are considered by vehicleclassifications (such as standard passenger cars and trucks). However, vehicleflow heterogeneity stems from many other aspects in general, e.g.,ride-sourcing vehicles versus personal vehicles, human driven vehicles versusconnected and automated vehicles. Provided with some observations of vehicularflow for each class in a large-scale transportation network, how to estimatethe multi-class spatio-temporal vehicular flow, in terms of time-varyingOrigin-Destination (OD) demand and path/link flow, remains a big challenge.This paper presents a solution framework for multi-class dynamic OD demandestimation (MCDODE) in large-scale networks. The proposed framework is built ona computational graph with tensor representations of spatio-temporal flow andall intermediate features involved in the MCDODE formulation. Aforward-backward algorithm is proposed to efficiently solve the MCDODEformulation on computational graphs. In addition, we propose a novel concept oftree-based cumulative curves to estimate the gradient of OD demand. A GrowingTree algorithm is developed to construct tree-based cumulative curves. Theproposed framework is examined on a small network as well as a real-worldlarge-scale network. The experiment results indicate that the proposedframework is compelling, satisfactory and computationally plausible.

Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs