Question

Exercise 1 [I8 pts]. Two lanes of a three-lane highway are closed because of road works on a 2 km long segment. A detector placed on one single lane in the undisturbed zone upstream the road works detects a flow of 2,000 veh/h and an average speed of 100 km/h. A second detector placed on one of the two lanes just upstream the roadwork zone detects a flow of 800 veh/h and an average speed of 40 km/h. We observe also that the traffic speed along the roadwork segment is 60 km/h and that the traffic stream reaches the limit speed after having left the roadwork zone. Determine: a) How long is the queue Q after 20 minutes from q-..... [unit of measure] the beginning of the roadworks? (2 Points) b) What is the traffic density along the roadwork k.. segment (2 Points) [unit of measure c) What is the traffic density downstream the roadwork segment? (2 Points) k2- unit of measure] d) Draw the fundamental diagram for the 3-lane segment and for the 1-lane segment. Identify all the different traffic states and the kinematic waves that connect them. Use the blank cell orn the right (2 Points)

Answer 1

Considering unrestricted/uncompromised flow conditions q_3 = q_1st laine + q_2nd lane + q_3rd lane = 2000 + 800 + 800 = 3600 veh/hr. K_3 = q_3/u_3 = 60 veh/km (congested flow) Actual undistorted flow = 2000 times 3 lanes veh/hr. = 6000 veh/hr. confused flow = 3600 veh/hr. halted flow = 6000 - 3600 veh/hr. = 2400 veh/hr. halted vehicles in 20 minutes = 800 vehicles. Q_max = K_j times V_SF/4 K_j = 4q_max/V_sF = 4 times 3600/100 = 144 veh/km. Therefore Q length = 800/144 = 5.56 km Traffic density downstream = ? q_4 downstream = 3600/3 = 1200 veh/hr. V_4 = 100 km/hr. K_4 = 1200/100 = 12 veh/km.