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Title: Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs
Authors: Ma, W 
Pi, X
Qian, S
Issue Date: Oct-2020
Source: Transportation research. Part C, Emerging technologies, Oct 2020, v. 119, 102747, p. 1-30
Abstract: Transportation networks are unprecedentedly complex with heterogeneous vehicular flow. Conventionally, vehicles are classified by size, the number of axles or engine types, e.g., standard passenger cars versus 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 that work for any vehicular data in general. The proposed framework cast the standard OD estimation methods into 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 compute the exact multi-class Dynamic Assignment Ratio (DAR) matrix. A Growing Tree algorithm is developed to construct tree-based cumulative curves. The proposed framework is examined on a small network, a mid-size network as well as a real-world large-scale network. The experiment results indicate that the proposed framework is compelling, satisfactory and computationally plausible.
Keywords: Dynamic networks
Machine learning
Multi-source data
Neural network
O-D estimation
Publisher: Pergamon Press
Journal: Transportation research. Part C, Emerging technologies 
ISSN: 0968-090X
DOI: 10.1016/j.trc.2020.102747
Rights: © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (
The following publication Ma, W., Pi, X., & Qian, S. (2020). Estimating multi-class dynamic origin-destination demand through a forward-backward algorithm on computational graphs. Transportation Research Part C: Emerging Technologies, 119, 102747 is available at
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