Question

Traffic on a section of an arterial road is flowing at a space mean speed of 40km/hr. The flow of traffic on the road section can be described using the following equation (where q represents flow in veh/hr and k represents the density in veh/km): q = 50 * (k - k^2/150) A slow moving heavy vehicle turns onto the roadway at 2pm, 2km from the beginning of the arterial road, driving at 15km/hr due to its heavy load. The vehicle impedes traffic; however, vehicles can pass the slow-moving vehicle resulting in an average space mean speed of 20km/hr upstream of the heavy vehicle. The heavy vehicles leaves the arterial road 15km after joining the traffic stream and at this point in time vehicles begin to move at the maximum flow rate. Use a space time-diagram and shock wave theory to describe this traffic event. Not all trajectories need to be presented; representative trajectories should be used to describe the flow across all the different traffic regions. Determine the speed of each shock wave, the points of intersection of each of the shockwaves and the time taken for the congestion to dissipate (maximum queue to be released).

Answer 1