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On the Distribution of Probe Traffic Volume Estimated without Trajectory Reconstruction

Kentaro Iio, Gulshan Noorsumar, Dominique Lord, Yunlong Zhang

TL;DR

This work presents the exact distribution of the estimated probe traffic volume in a road segment based on probe point location data without trajectory reconstruction, which can exhibit multimodality, without necessarily being line-symmetric with respect to the true probe traffic volume.

Abstract

In recent years, passively recorded probe traffic volumes have increasingly been used to estimate traffic volumes. However, it is not always possible to count probe traffic volume in a spatial dataset when probe trajectories cannot be fully reconstructed from raw probe point location data due to sparse recording intervals, lack of pseudonyms or timestamps. As a result, the application of such probe point location data has been limited in traffic volume estimation. To relax these constraints, we present the exact distribution of the estimated probe traffic volume in a road segment based on probe point location data without trajectory reconstruction. The distribution of the estimated probe traffic volume can exhibit multimodality, without necessarily being line-symmetric with respect to the true probe traffic volume. As more probes are present, the distribution approaches a normal distribution. The conformity of the distribution was visualised through numerical simulations. Sometimes, there exists a local optimal cordon length that maximises estimation precision. The theoretical variance of estimated probe traffic volume can address heteroscedasticity in the modelling of traffic volume estimates.

On the Distribution of Probe Traffic Volume Estimated without Trajectory Reconstruction

TL;DR

This work presents the exact distribution of the estimated probe traffic volume in a road segment based on probe point location data without trajectory reconstruction, which can exhibit multimodality, without necessarily being line-symmetric with respect to the true probe traffic volume.

Abstract

In recent years, passively recorded probe traffic volumes have increasingly been used to estimate traffic volumes. However, it is not always possible to count probe traffic volume in a spatial dataset when probe trajectories cannot be fully reconstructed from raw probe point location data due to sparse recording intervals, lack of pseudonyms or timestamps. As a result, the application of such probe point location data has been limited in traffic volume estimation. To relax these constraints, we present the exact distribution of the estimated probe traffic volume in a road segment based on probe point location data without trajectory reconstruction. The distribution of the estimated probe traffic volume can exhibit multimodality, without necessarily being line-symmetric with respect to the true probe traffic volume. As more probes are present, the distribution approaches a normal distribution. The conformity of the distribution was visualised through numerical simulations. Sometimes, there exists a local optimal cordon length that maximises estimation precision. The theoretical variance of estimated probe traffic volume can address heteroscedasticity in the modelling of traffic volume estimates.
Paper Structure (16 sections, 5 theorems, 14 equations, 8 figures)

This paper contains 16 sections, 5 theorems, 14 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Probe Data in Traffic Volume Estimation
  3. Types of Probe Data
  4. Theory
  5. Problem Statement
  6. Unbiased Estimator of $m$
  7. Example 1
  8. Variance of $\hat{m}$
  9. Example 2
  10. Shape of $\hat{m}$
  11. Example 3
  12. Optimal Cordon Length
  13. Example 4
  14. Simulations
  15. Method
  16. ...and 1 more sections

Key Result

Lemma 1

If we define $\hat{m}$ as $\hat{m}$ is an unbiased estimator of the true probe traffic volume $m$ (Equation eq:kgbnho).

Figures (8)

  • Figure 1: Illustrated virtual cordons over probe point data and line data (reconstructed trajectories).
  • Figure 2: An illustrated example of a virtual cordon over point data ($m = 2$).
  • Figure 3: Variance derivation when $d$ = 300, $t$ = 4, and $S \sim g(s)$.
  • Figure 4: $\hat{m}$ as a function of $s$ and $k$ when $d$ = 300, $t$ = 4, and $m$ = 1.
  • Figure 5: The PMFs of $Ber(p)$ weighted by $g(s)$ as a function of $s$ and $k$ when $d$ = 300 and $t$ = 4.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Corollary 1
  • Corollary 2