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.
Keywords : Fundamental Diagram, Moving bottleneck, Phase transitions, Traffic flow, Three phase traffic flow.
