The Effects of Car Density on the Overall Interaction of the Vehicles Current Traffic Flow Models Case Study at Wolaita Sodo Town

Abstract

Congestion of vehicular traffic within urban areas is a problem experienced worldwide. It has adverse effects on people quality of life due to delays, accidents and environmental pollution. Congestion is gaining popularity in the Wolaita Sodo and quantifying the effects of an additional vehicle joining the traffic stream is a critical issue to determine the toll rates. When additional vehicles enter a crowded roadway they increase travel time for all vehicles. The effect of additional vehicles worsens when the flow is near the capacity of the traffic stream. The speed and flow of the traffic stream are considered as the major variables to quantify these effects. Hence to better understand and quantify this issue it is necessary to accurately model the traffic stream near capacity. A mathematical macroscopic traffic flow model known as Lighthill, Whitham and Richards model appended with a closure nonlinear velocity-density relationship yielding a quasi-linear first order (hyperbolic) partial differential equation as an initial boundary value problem was considered. The aims of this analysis are principally represented by the maximization of vehicles flow, and the minimization of traffic congestions, accidents and pollutions. We  present  numerical simulation  of  the  IBVP  by  a  finite  difference  scheme report  on  the stability and efficiency of the scheme by performing numerical experiments. The computed result satisfies some well known qualitative features of the solution.

Keywords: Density function , quasi-linear, Macroscopic Traffic flow, Numerical simulation.