Mixed Vehicular Traffic Flow Model on an Inclined Multilane Road

Abstract

This study outlines the Kerner’s 3 phase traffic flow theory, which states that traffic flow occurs in three phases and these are free flow, synchronized flow and wide moving jam phase. A macroscopic traffic model that is factoring road inclination is developed and its features discussed. By construction of the solution to the Rienmann problem, the model is written in conservative form and solved numerically. Using the Lax-Friedrichs method and going ahead to simulate traffic flow on an inclined multi lane road. The dynamics of traffic flow involving cars(fast moving) and trucks(slow moving) on a multi-lane inclined road is studied. Generally, trucks move slower than cars and their speed is significantly reduced when they are moving uphill on an in- clined road, which leads to emergence of a moving bottleneck. If the inclined road is multi-lane then the cars will tend to change lanes with the aim of overtaking the slow moving bottleneck to achieve free flow. The moving bottleneck and lanechange ma- noeuvres affect the dynamics of flow of traffic on the multi-lane road, leading to traffic phase transitions between free flow (F) and synchronised flow(S). Therefore, in order to adequately describe this kind of traffic flow, a model should incorporate the effect of road inclination. This study proposes to account for the road inclination through the fundamental diagram, which relates traffic flow rate to traffic density and ultimately through the anticipation term in the velocity dynamics equation of macroscopic traffic flow model. The features of this model shows how the moving bottleneck and an incline multilane road affects traffic transistions from Free flow(F) to Synchronised flow(S). For a better traffic management and control, proper understanding of traffic congestion is needed. This will help road designers and traffic engineers to verify whether traffic properties and characteristics such as speed(velocity), density and flow among others determines the effectiveness of traffic flow.