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