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

arXiv: https://arxiv.org/abs/1903.04681 · HTML: https://mlsanity.com/paper/1903.04681/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2019.

## Built on by (most cited first, 10 of 10)

- [Exploring the Roles of Large Language Models in Reshaping Transportation Systems: A Survey, Framework, and Roadmap](https://mlsanity.com/paper/2503.21411/) (2025)
- [Real-time system optimal traffic routing under uncertainties -- Can physics models boost reinforcement learning?](https://mlsanity.com/paper/2407.07364/) (2024)
- [Estimating and Mitigating the Congestion Effect of Curbside Pick-ups and Drop-offs: A Causal Inference Approach](https://mlsanity.com/paper/2206.02164/) (2022)
- [Traffic estimation in unobserved network locations using data-driven macroscopic models](https://mlsanity.com/paper/2401.17095/) (2024)
- [Network-wide link travel time and station waiting time estimation using automatic fare collection data: A computational graph approach](https://mlsanity.com/paper/2108.09292/) (2021)
- [Cyclic Graph Attentive Match Encoder (CGAME): A Novel Neural Network For OD Estimation](https://mlsanity.com/paper/2111.14625/) (2021)
- [Scalable Dynamic Origin-Destination Demand Estimation Enhanced by High-Resolution Satellite Imagery Data](https://mlsanity.com/paper/2506.22499/) (2025)
- [Ultra-fast Traffic Nowcasting and Control via Differentiable Agent-based Simulation](https://mlsanity.com/paper/2603.25068/) (2026)
- [Metropolis-Scale Resilient and Trustworthy Traffic Flow Inference Using Multi-Source Data](https://mlsanity.com/paper/2605.25004/) (2026)
- [Online Estimation of Dynamic Origin-Destination Matrices Using Reinforcement Learning with Link-Flow Propagation Guidance](https://mlsanity.com/paper/2608.30317/) (2026)

## Abstract (arXiv)

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.