Abstract
The fundamental relationship of traffic flow and bivariate relations between speed and flow, speed and density, and flow and density are of great importance in transportation engineering. Fundamental relationship models may be applied to assess and forecast traffic conditions at uninterrupted traffic flow facilities. The objective of the article was to analyze and compare existing models of the fundamental relationship. To that end, we proposed a universal and quantitative method for assessing models of the fundamental relationship based on real traffic data from a Polish expressway. The proposed methodology seeks to address the problem of finding the best deterministic model to describe the empirical relationship between fundamental traffic flow parameters: average speed, flow, and density based on simple and transparent criteria. Both single and multi-regime models were considered: a total of 17 models. For the given data, the results helped to identify the best performing models that meet the boundary conditions and ensure simplicity, empirical accuracy, and good estimation of traffic flow parameters.
Highlights
Traffic flow models describe vehicle flows using three basic parameters: average speed (v), density (k), and flow (q)
When traffic flow is considered a stationary phenomenon, the parameters are linked with one another using a relationship (1), which is known as the fundamental relationship
The relationship (1) and bivariate relations between speed and flow, speed and density, and flow and density are of great importance in transportation engineering. They are used in planning, design and redesign, operation, and control of transportation facilities; they help to determine the actual capacity of an existing road, assess its traffic conditions or select the cross-section for a new road depending on forecasted traffic volumes
Summary
Traffic flow models describe vehicle flows using three basic parameters: average speed (v), density (k), and flow (q). The relationship (1) and bivariate relations between speed and flow, speed and density, and flow and density are of great importance in transportation engineering They are used in planning, design and redesign, operation, and control of transportation facilities; they help to determine the actual capacity of an existing road, assess its traffic conditions or select the cross-section for a new road depending on forecasted traffic volumes. Researchers have been exploring ways to offer the best possible mathematical description of the relations. These were established either empirically by looking for mathematical models that fit the observed data or derived from microscopic traffic flow characteristics or from the analogy to the movement of fluid. Since they are simple to use, interpret, and determine traffic characteristics, the models have a wide variety of applications, including methods for forecasting and assessing traffic conditions
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