Question 5- Combined moving bottleneck and fixed bottleneck [32] The volume at a section of a single-lane highway is 1000 veh/h and the speed is 100 km/h in each direction. A large dump truck joins the traffic stream and travels at a speed of 20 km/h for a length of 1 km along the road before arriving at a signalised intersection. Due to the relatively high flow in the opposite direction, it is impossible for any car to pass the truck. Vehicles behind the truck, therefore, have to travel at the speed of the truck which results in the formation of congestion (ie moving bottleneck). When the truck arrives at the intersection, the signal turns red. After 90 seconds, the signal turns green and the truck begins to move at the same speed of 20 km/hr as before. The truck leaves the highway 1 km downstream of the intersection. After the truck leaves the highway, traffic will reach the capacity of 2400 veh/h. Assuming a triangular shape of the flow-density relationship with a jam density of 160 veh/km. a) Identify traffic states (flow and density) on the above hichwav [6] b) Calculate the shockwave speeds and plot the shockwaves v wie fundamental diagram [6] c) Plot the time-space diagram, corresponding to vehicles following the truck when it enters and leaves the highway, showing the shockwaves in this time-space diagram [6] d) Sketch some approximate vehicle trajectories on the time-space diagram [4] e) Determine the length of the queue (in km) behind the truck at the beginning of the red signal [2] f) Determine the length of the queue (in km) behind the truck at the end of the red signal [8] Hint: prove that the first two shockwaves intersect before the signal turns green