Fine-grained OD estimation with automated zoning and sparsity regularisation

Given a road network, a fundamental object of interest is the matrix of origin destination (OD) flows. Estimation of this matrix involves at least three sub-problems: (i) determining a suitable set of traffic analysis zones, (ii) the formulation of an optimisation problem to determine the OD matrix, and (iii) a means of evaluating a candidate estimate of the OD matrix. This paper describes a means of addressing each of these concerns. We propose to automatically uncover a suitable set of traffic analysis zones based on observed link flows. We then employ regularisation to encourage the estimation of a sparse OD matrix. We finally propose to evaluate a candidate OD matrix based on its predictive power on held out link flows. Analysis of our approach on a real-world transport network reveals that it discovers automated zones that accurately capture regions of interest in the network, and a corresponding OD matrix that accurately predicts observed link flows. 2015 Elsevier Ltd. All rights reserved. 1. Problem statement Origin–destination (OD) flows are a fundamental object of interest in the study of urban transportation networks (Ortuzar and Willumnsen, 2011, Chapter 5). In principle, these are the steady-state flow of traffic between any pair of traffic intersections. In practice, one instead considers the steady-state flow of traffic between any pair of traffic analysis zones (henceforth simply zones). A zone represents an aggregation of intersections in the underlying network, and offers conceptually and computationally simpler modelling. More formally, consider a directed graph G representing a road network, where the nodes in the graph represent traffic intersections, and the links represent road segments between intersections. We denote the set of nodes by N and the set of links by L, and will often write G 1⁄4 ðN;LÞ. Suppose also that there is a vector y 2 NjLj þ , representing the count of steady-state traffic flow on each road segment over some time period (e.g. the morning rush hour). To analyse OD flows, one defines a special set of virtual nodes Nvirt, which are connected via a number of virtual links Lvirt to nodes in N. The set of traffic analysis zones Z is simply the set of virtual nodes and their corresponding virtual links, so that each virtual node represents the focal point of an individual zone. Given Z, the origin–destination matrix (OD matrix) X of size jZj jZj represents, for any pair of zones ðz; z0Þ 2 Z Z, the steady-state flow of traffic that begins at zone z and ends at zone z0.