Modeling Vehicle Traffic Flow between Traffic Light Nodes with Partial Differential Equations
Loading...
Date
2013-06-17
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Vehicle traffic flow has become a challenge in this modern world of automobiles due to constantly accelerated influx of vehicles on the road network. The challenge of traffic flow has motivated many researchers to model traffic flow at both the macroscopic and microscopic levels. In order to ensure free flow of vehicles in the cities, road engineers have developed and implemented traffic lights to regulate the inflow and outflow of vehicles at the major intersections of road. However, the traffic lights have become one the major causes of traffic jams in the cities since they force the vehicles to stop causing a discontinuity of flow. This study seeks to model the continuous and the discontinuous behaviour of vehicles by the parameters: flow, density and velocity between two given traffic light nodes in Kumasi, Ghana with the use of partial differential Equations (PDEs) based on Lighthill, Whitham and Richard (LWR) model. Primary data was obtained from the study zone, a 100m road segment in Kumasi, during the peak hour in the morning .The flow was regressed on the density and the result indicated a quadratic dependence between flow and density confirming the fundamental relation of Greenshield. With prescribed initial conditions, the first order nonlinear homogeneous and nonlinear inhomogeneous PDE’s models were solved using the method of characteristics.
Description
A thesis submitted to the Institute of Distance Learning, Kwame Nkrumah University of Science and Technology in partial fulfilment of the requirement for the award of Master of Science degree in Industrial Mathematics, June-2013