An arterial road having three lanes in each direction carries traffic quite well in the evening peak period until a car illegally parks, blocking one of the three lanes and forcing traffic to merge into the other two lanes. A traffic queue quickly builds up behind the parked car. The fundamental diagram for this road can be modelled using a triangular flow-density relationship, having a capacity (maximum flow) of 4500 vehicles per hour, a critical density of 100 vehicles per kilometre, and a jam density of 300 vehicles per kilometre. Note also that this road has three lanes. Assuming that the parked car remains and after a period of 45 minutes the arrival flow decreases from 3500 vehicles per hour to 2000 vehicles per hour. a) Identify traffic states (flow and density) on the above arterial road. Calculate the shockwave speeds and plot the shockwaves on the fundamental diagram. Plot the time-space diagram with some vehicle trajectories and showing the shockwaves in this time-space diagram. b) Calculate the queue of slow-moving vehicles reach in the 45 minutes until the arrival flow decreases. Calculate the time it takes the queue of slow-moving vehicles to dissipate after the arrival flow decreases.
An arterial road having three lanes in each direction carries traffic quite well in the evening peak period until a car illegally parks, blocking one of the three lanes and forcing traffic to merge into the other two lanes. A traffic queue quickly builds up behind the parked car. The fundamental diagram for this road can be modelled using a triangular flow-density relationship, having a capacity (maximum flow) of 4500 vehicles per hour, a critical density of 100 vehicles per kilometre, and a jam density of 300 vehicles per kilometre. Note also that this road has three lanes. Assuming that the parked car remains and after a period of 45 minutes the arrival flow decreases from 3500 vehicles per hour to 2000 vehicles per hour.
a) Identify traffic states (flow and density) on the above arterial road. Calculate the shockwave speeds and plot the shockwaves on the fundamental diagram. Plot the time-space diagram with some vehicle trajectories and showing the shockwaves in this time-space diagram.
b) Calculate the queue of slow-moving vehicles reach in the 45 minutes until the arrival flow decreases. Calculate the time it takes the queue of slow-moving vehicles to dissipate after the arrival flow decreases.
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