Estimation methods for fundamental and topological parameters in area-wide macroscopic traffic flow models

Abstract

Area-wide macroscopic traffic flow models have recently drawn a great deal of attention due to their tremendous potential benefits in various applications, such as network traffic control and initial land use planning. These models can be generally classified into two categories: (a) area-wide macroscopic cost flow (MCF) functions and (b) area-wide macroscopic fundamental diagrams (MFDs). For this study’s in-depth examinations, the selected MCF functions are the macroscopic Bureau of Public Road (MBPR) functions, and the selected MFDs are macroscopic Underwood models. For the beneficial application of these models, the prerequisite is to obtain well-established, accurate, area-wide macroscopic traffic flow models. However, due to various limitations of the high-tech detectors and sensors used in direct area-wide traffic data collection, it remains challenging to estimate these models based on real-world traffic data.

This study develops estimation methods for the two classes of area-wide macroscopic traffic flow models that use two different approaches. In the first approach, direct methods for estimating the fundamental parameters and standard errors of these models (based on traffic data) are evaluated by using linear data projection. Linear data projection is a timely, commonly adopted data scaling method that can compatibly fuse data from various sources for unbiased traffic data estimations. This projection can infer unobservable traffic data by projecting the observable traffic data, using the mean of a set of scaling factors. Linearly projected data may be unbiased in nature, but direct model calibrations based on such data without considering the effects of scaling factor variability can lead to systematically biased estimates of parameters and standard errors. This study unveils the origin of such biases, and it generically proves the necessary and the sufficient conditions for their introduction. To remove or reduce such biases, different estimation methods are proposed that can incorporate the higher order moments of the scaling factors for the two classes of models. Simulations reveal that the proposed methods can accurately estimate the parameters and standard errors. To illustrate these methods, MBPR functions and macroscopic Underwood models are estimated for networks sampled from Hong Kong, according to the proposed methods, with the use of traffic data retrieved from global positioning system-equipped taxis and counting stations.

The second approach is to establish indirect estimation methods for the two classes of area-wide macroscopic traffic flow models by using network topological metrics as inputs. Area-wide macroscopic traffic flow models depict a network’s performance at different levels of traffic demand and at different loadings. Network topologies are apparently the primary factors determining the shapes of these models. This study identifies the determining topological factors, and unveils their relationships with the parameters of the two classes of models based on empirical data. By applying these unveiled relationships, the spatially variable area-wide macroscopic traffic flow models can be established. These models provide simple, fast, straightforward alternatives to the estimations of MCF functions and MFDs using the governing topological metrics. Compared with traffic data, network topological data are much more easily obtainable, and therefore substantially simplify the estimation procedures for these models.