Loading...

Extension of the Macroscopic Traffic Flow Model

Mohammad Pour, Ismael | 2019

1050 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51889 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Nassiri, Habibollah
  7. Abstract:
  8. Traffic flow modeling on different levels was always the topic of many studies. In this regard, many researchers have tried to eliminate traffic problems by developing precise models. Therefore, in this study and in its two major parts, we developed two models: one macroscopic and one microscopic. Like previous studies, the main purpose here was the development of traffic flow models that have better precision and give more information about the mechanism behind the traffic phenomena. Our focus was on the free spaces in front of drivers which were considered in a macroscopic traffic flow model and resulting microscopic traffic flow model.First part, addresses the first-order extension of the Lighthill-Whitham-Richards (LWR) macroscopic traffic flow model. Although previous studies have focused on the fluid aspect of traffic flow, none have addressed the sensitivity of drivers to the number of free spaces within a certain distance ahead of the subject driver. To incorporate driver behavior, we used the number of free spaces ahead of subject drivers and their sensitivity to the number of free spaces within a certain distance ahead. The resulting model is a convection-diffusion model. By computing Einstein’s diffusion equation and comparing it with the diffusion coefficient in the extended model, a theoretical relation for the driver’s sensitivity was derived. A representation of the numerical results of the LWR model, the convection-diffusion model with a typical diffusion coefficient, and the extended model showed that the proposed model has a lower mean relative error value. An advantage of the proposed model is that it does not add an extra initial or boundary condition. Optimizing the new extended model results in an average distance ahead of drivers of 100 m and their sensitivity to this distance is 0.145 s 1.In the second part, we used the calculated diffusion coefficient in macroscopic traffic flow models which results from Einstein’s diffusion equation. This coefficient is also calculated by using microscopic variables: the number of the free spaces ahead of the driver and driver sensitivity. By equating these two coefficients, the derived driver sensitivity relation was used in a car-following model in which the number of free spaces plus the desired distance is equal to the distance between the following and leading vehicles. The theoretical properties of the resulting car-following model were explored in three scenarios. First, when the leaders position function is linear, the follower’s position function eventually becomes linear. Second, when the leading vehicle is stopped, the speed of the following vehicle tends towards zero as time tends towards infinity. Finally, when the initial speed of the following vehicle is zero, by adding a helping term the following vehicle’s trajectory recovers from zero. Moreover, the systems of vehicles also considered for analyzing the traffic perturbations. At the end, NGSIM data were used for an example of model’s application on the real world data.Results of the first part shows that using free spaces ahead of drivers and their sensitivity to this parameter, we can develop a macroscopic model with more degrees of freedom which gives better approximations. Finally, the second part shows that the resulting microscopic traffic flow model also have satisfying results. Error analysis in the first part shows that the resulting model has lower errors, and in the second part, the proposed model can simulate real world traffic data
  9. Keywords:
  10. Macroscopic Traffic Flow Model ; Diffusion Coefficient ; Free Space Ahead ; Driver Sensitivity ; Microscopic Traffic Flow Model

 Digital Object List

 Bookmark

...see more