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Arc travel time and path choice model estimation subsumed

Sobhan Mohammadpour, Emma Frejinger

TL;DR

This work tackles the problem of simultaneously estimating arc travel times $\boldsymbol{T}$ and route-choice parameters $\boldsymbol{b}$ for road networks, addressing the interdependence between travel-time estimation and path choice. It introduces a mixture likelihood that accommodates observations at varying granularities, including partially observed paths, and derives differentiable, gradient-based optimization compatible with any differentiable route-choice model. Through synthetic data and the NYC Yellow Cab dataset, the approach demonstrates competitive travel-time accuracy and superior parameter recovery relative to two-step baselines, while remaining scalable to large networks. The method also highlights practical benefits of mixing data types and provides a flexible framework for extending to time-varying networks and more complex route-choice formulations.

Abstract

We address the problem of simultaneously estimating arc travel times in a network \emph{and} parameters of route choice models for strategic and tactical network planning purposes. Hitherto, these interdependent tasks have been approached separately in the literature on road traffic networks. We illustrate that ignoring this interdependence can lead to erroneous route choice model parameter estimates. We propose a method for maximum likelihood estimation to solve the simultaneous estimation problem that is applicable to any differentiable route choice model. Moreover, our approach allows to naturally mix observations at varying levels of granularity, including noisy or partial path data. Numerical results based on real taxi data from New York City show strong performance of our method, even in comparison to a benchmark method focused solely on arc travel time estimation.

Arc travel time and path choice model estimation subsumed

TL;DR

This work tackles the problem of simultaneously estimating arc travel times and route-choice parameters for road networks, addressing the interdependence between travel-time estimation and path choice. It introduces a mixture likelihood that accommodates observations at varying granularities, including partially observed paths, and derives differentiable, gradient-based optimization compatible with any differentiable route-choice model. Through synthetic data and the NYC Yellow Cab dataset, the approach demonstrates competitive travel-time accuracy and superior parameter recovery relative to two-step baselines, while remaining scalable to large networks. The method also highlights practical benefits of mixing data types and provides a flexible framework for extending to time-varying networks and more complex route-choice formulations.

Abstract

We address the problem of simultaneously estimating arc travel times in a network \emph{and} parameters of route choice models for strategic and tactical network planning purposes. Hitherto, these interdependent tasks have been approached separately in the literature on road traffic networks. We illustrate that ignoring this interdependence can lead to erroneous route choice model parameter estimates. We propose a method for maximum likelihood estimation to solve the simultaneous estimation problem that is applicable to any differentiable route choice model. Moreover, our approach allows to naturally mix observations at varying levels of granularity, including noisy or partial path data. Numerical results based on real taxi data from New York City show strong performance of our method, even in comparison to a benchmark method focused solely on arc travel time estimation.
Paper Structure (25 sections, 4 theorems, 28 equations, 10 figures, 4 tables)

This paper contains 25 sections, 4 theorems, 28 equations, 10 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. A Method for Arc Travel Time Estimation
  4. Route Choice Models
  5. Motivating Example: Two Arcs, One Hard Network
  6. Methodology
  7. A Mixture to Model Observations at Different Granularities
  8. Solution Approach
  9. A Worked Example
  10. Details
  11. Inference.
  12. Domain of $\boldsymbol{T}$.
  13. Identifiability.
  14. Regularization.
  15. Optimization.
  16. ...and 10 more sections

Key Result

Proposition 1

For any function $L:\mathbb{D}\times\Theta\rightarrow\mathbb{R}$, defined over the observation domain $\mathbb{D}$ and the parameter space $\Theta$, let, for a parameter vector $\theta$ in $\Theta$, be the partition function. Whenever $Z_L(\theta)$ converges, is a valid pdf. Furthermore, if $Z_L$ is a constant independent of $\theta$, the log-likelihood of the distribution corresponding to $f_L$

Figures (10)

  • Figure 1: Overview of data, travel time and route choice model estimation and their link to network planning problems
  • Figure 2: Network and noise model visualization.
  • Figure 3: A simple network with a trajectory that originates at a or b, pass through c, and end at e.
  • Figure 4: Comparison of estimated arc travel time matrix, same color scale for all figure. reg. stands for regularized.
  • Figure 5: Cumulative distribution of the ratio of sampled paths and shortest path travel times.
  • ...and 5 more figures

Theorems & Definitions (7)

  • Proposition 1
  • Remark 1
  • Remark 2
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Remark 3