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A Dynamic Programming Approach for Road Traffic Estimation

Mattia Laurini, Irene Saccani, Stefano Ardizzoni, Luca Consolini, Marco Locatelli

TL;DR

The paper addresses OD traffic tomography on a known road network by modeling arc flows as a sum of independent Poisson processes and inferring both path choices and Poisson means. It introduces a dynamic programming approach that leverages higher-order cumulants via cumulant generating functions, enabling efficient identification of active paths and estimates of mean demands. The method is theoretically grounded, detailing a partial order on path sets and a monotone cumulant-based framework, and is validated through simulations on NSFnet and Sioux Falls networks using synthetic data. The work highlights computational considerations when using higher-order cumulants and points to robustness as a future direction, with practical impact on traffic planning and network usage analysis.

Abstract

We consider a road network represented by a directed graph. We assume to collect many measurements of traffic flows on all the network arcs, or on a subset of them. We assume that the users are divided into different groups. Each group follows a different path. The flows of all user groups are modeled as a set of independent Poisson processes. Our focus is estimating the paths followed by each user group, and the means of the associated Poisson processes. We present a possible solution based on a Dynamic Programming algorithm. The method relies on the knowledge of high order cumulants. We discuss the theoretical properties of the introduced method. Finally, we present some numerical tests on well-known benchmark networks, using synthetic data.

A Dynamic Programming Approach for Road Traffic Estimation

TL;DR

The paper addresses OD traffic tomography on a known road network by modeling arc flows as a sum of independent Poisson processes and inferring both path choices and Poisson means. It introduces a dynamic programming approach that leverages higher-order cumulants via cumulant generating functions, enabling efficient identification of active paths and estimates of mean demands. The method is theoretically grounded, detailing a partial order on path sets and a monotone cumulant-based framework, and is validated through simulations on NSFnet and Sioux Falls networks using synthetic data. The work highlights computational considerations when using higher-order cumulants and points to robustness as a future direction, with practical impact on traffic planning and network usage analysis.

Abstract

We consider a road network represented by a directed graph. We assume to collect many measurements of traffic flows on all the network arcs, or on a subset of them. We assume that the users are divided into different groups. Each group follows a different path. The flows of all user groups are modeled as a set of independent Poisson processes. Our focus is estimating the paths followed by each user group, and the means of the associated Poisson processes. We present a possible solution based on a Dynamic Programming algorithm. The method relies on the knowledge of high order cumulants. We discuss the theoretical properties of the introduced method. Finally, we present some numerical tests on well-known benchmark networks, using synthetic data.
Paper Structure (16 sections, 6 theorems, 34 equations, 5 figures, 1 algorithm)

This paper contains 16 sections, 6 theorems, 34 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Statement of contribution
  4. Paper organization
  5. Notation
  6. Problem formulation
  7. Problem 1: we know $A$ and the statistics of $Y$
  8. Problem 2: we only know the statistics of $Y$
  9. Example of Algorithm \ref{['alg:DP']} execution
  10. Traffic demand and path estimation from flow data
  11. Problem 1: we observe all flows
  12. Problem 2: we observe a subset of flows
  13. Simulation results on synthetic data
  14. NSFnet
  15. Sioux Falls
  16. ...and 1 more sections

Key Result

Proposition 2.1

Functions $f_1,\ldots,f_q$ are independent if and only if all columns of $A$ are different.

Figures (5)

  • Figure 1: Graph associated with matrix $A$ of \ref{['eq:exampleAX']}.
  • Figure 2: Graph of NSFnet.
  • Figure 3: Relative error for 100 tests, on number of measurements. The means for each number of measurements are depicted in red.
  • Figure 4: Graph of Sioux Falls.
  • Figure 5: Relative error for 100 tests, on number of measurements. The means for each number of measurements are depicted in red.

Theorems & Definitions (15)

  • Proposition 2.1
  • Proposition 2.2
  • Proposition 2.3
  • proof
  • Example 2.4
  • Proposition 2.5
  • proof
  • Definition 2.6
  • Example 2.7
  • Definition 2.8
  • ...and 5 more