Estimation of an Origin/Destination matrix: Application to a ferry transport data

TL;DR

This paper introduces a new statistical method for estimating origin-destination matrices in public transport using partial data and surveys, without requiring prior OD matrices, and demonstrates its robustness and flexibility.

Contribution

The paper provides a novel framework for OD matrix estimation that integrates survey data and partial counts, avoiding the need for prior OD matrices and allowing incorporation of additional variables.

Findings

Robustness of the estimator demonstrated across multiple examples

Method effectively integrates survey data and partial counts

Incorporates additional explanatory variables like rainfall and events

Abstract

The estimation of the number of passengers with the identical journey is a common problem for public transport authorities. This problem is also known as the Origin- Destination estimation (OD) problem and it has been widely studied for the past thirty years. However, the theory is missing when the observations are not limited to the passenger counts but also includes station surveys. Our aim is to provide a solid framework for the estimation of an OD matrix when only a portion of the journey counts are observable. Our method consists of a statistical estimation technique for OD matrix when we have the sum-of-row counts and survey-based observations. Our technique differs from the previous studies in that it does not need a prior OD matrix which can be hard to obtain. Instead, we model the passengers behavior through the survey data, and use the diagonalization of the partial OD matrix to reduce the space parameter and derive a consistent global OD matrix estimator. We demonstrate the robustness of our estimator and apply it to several examples showcasing the proposed models and approach. We highlight how other sources of data can be incorporated in the model such as explanatory variables, e.g. rainfall, indicator variables for major events, etc, and inference made in a principled, non-heuristic way.