A heuristic for the bilevel origin–destination-matrix estimation problem

Abstract

In this paper we consider the estimation of an origin-destination (OD) matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the wellknown projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks.

The price of anarchy in transportation networks by estimating user cost functions from actual traffic data

“…In particular, [26] proposed a Generalized Least Squares (GLS) method to estimate the OD demand matrices of uncongested networks, and [11,27,12] considered networks that could include congested roads.…”

“…In particular, we can solve the user-centric forward problem (2), embedded in a typical GPS navigation application, with t a (·) replaced by t a (·), whose common cornerstone part, f (·), is estimated using (12). It is worth pointing out that some existing work simply took f (·) to be the Bureau of Public Roads (BPR)'s [7] empirical polynomial function f (z) = 1 + 0.15z 4 , ∀z ≥ 0, which would not be as accurate.…”

A Kalman Filter Approach for Exploiting Bluetooth Traffic Data When Estimating Time-Dependent OD Matrices

“…Then, they are adjusted from the available link counts provided by an existing layout of traffic counting stations and other additional information whenever it is available. Adjustments can be considered as indirect estimation methods, based either on discrete time optimization approaches (Codina & Barceló (2004); Lundgren & Peterson (2008)) or on adaptations of Kalman Filtering approaches (Ashok & Ben Akiva, 2000;Antoniou, BenAkiva & Koutsopoulos, 2007;Barceló et al 2010a We placed flow counting detectors and ICT sensors in a cordon and at each possible point for flow entry (centroids of the study area). ICT sensors were located at intersections in urban networks and covered access and links to/from the intersection.…”

A Least-Square Model to Estimate Historical Percentages of Itinerant General Aviation Operations by Aircraft Types and Flight Rules at an Airport

“…These methods could produce relatively accurate and cost-beneficial estimates [10,23]. It is worthwhile to point out that models that utilize posterior observations have also been developed to estimate the historical demand in commercial air transportation (see, e.g., Li et al [24]; Li and Baik [25]; Li [26]; Li et al [27]; and Li [28]) and ground transportation (see, e.g., Maher [29]; Cascetta [30]; Bell [31]; Yang et al [32]; Codina and Barceló [33]; Chootinan et al [34]; Doblas and Benitez [35]; Nie et al [36]; Lundgren and Peterson [37]; Chen et al [38]). …”