| dc.description.abstract | Mathematical modeling of motor vehicle traffic flow systems and transportation processes taking into account of the dimensional properties of the roads, vehicle types, driver characteristics and flow properties leads to 2D heterogeneous motor vehicle traffic flow model equation with first order derivatives in two independent spatial variables and one temporal variable, time. The old models such as the Lighthill, Whitham and Richards, Van Tri Nguyen, Petrosyan and Balabanyan models were one dimensional and hence homogeneous. The effects of homogeneity resulted to regular head on accidents, head- to-back collisions, skidding at sharp corners, traffic congestion and increase in traveling time. Due to the pot holes realized in the old models there was need to work with heterogeneous motor vehicle traffic flow models so as to take care of dimensional, road, vehicle and driver heterogeneity aspects. The 2D heterogeneous motor vehicle traffic flow model was developed and used to investigate the effects of varying time and motor vehicle velocity on traffic flow density. This equation that governs the number of vehicles moving on the road was solved numerically by Finite Difference Method using Matrix Laboratory computer software program. The concepts of consistency and stability of the motor vehicle traffic flow model were analyzed. The study found out that the numerical schemes were consistent implying that the model equation can be recovered from the set of algebraic equations of the schemes developed. John Von Neumann Method was used to analyze the stability of the schemes developed and the schemes were found to be unconditionally stable. The numerical results obtained from the study revealed that an increase in time causes an increase in the traffic density per unit road length while an increase in motor vehicle velocity causes the traffic density to decrease. This study is a significant contribution to mechanical engineering, computer programming, town planning, transportation forecasting and Mathematical knowledge with hopes that the results obtained will find important applications going forward. | en_US |