Question

A four-lane highway has a normal capacity of 1800 veh/hr/lane. In the southbound direction, a vehicle disablement on the roadway shoulder occurs at 4:30 p.m. Due to bottlenecking, the capacity in the southbound direction is reduced to 1,200 veh/hr/lane at this time. At 4:45 p.m., the disabled vehicle is removed from the shoulder and the capacity increases to 1,500 veh/hr/lane. At 5:00 p.m., the roadway capacity returns to its full value of 1,800 veh/hr/lane. From 4:30 p.m. until the queue clears, the traffic flow is 1,600 veh/hr/lane. Determine the following:

(a) average delay per vehicle
(b) maximum queue length
(c) average queue length in the southbound direction?

Answer 1

The average delay per vehicle is 0.000625 hr/vehicle, the maximum queue length is 400 vehicles, and the average queue length in the southbound direction is 700 vehicles.

Step-by-step explanation:

To calculate the average delay per vehicle, we first need to find the difference between the normal capacity and the reduced capacity of the highway. The difference is 1800 - 1200 = 600 veh/hr/lane. From 4:30 p.m. until the queue clears at 5:00 p.m., a period of 30 minutes, the traffic flow is 1600 veh/hr/lane. Therefore, the total number of vehicles queued during this time is (1600 - 1200) * 4 lanes * 0.5 hr = 800 vehicles. The average delay per vehicle is the total delay time divided by the number of vehicles, which is 0.5 hr / 800 vehicles = 0.000625 hr/vehicle.

To calculate the maximum queue length, we need to find the maximum number of vehicles queued at a given time. At 4:30 p.m., the queue starts building up at a rate of (1600 - 1200) * 4 lanes = 1600 vehicles/hr. From 4:30 p.m. to 4:45 p.m., a period of 15 minutes, the number of vehicles queued is 1600 vehicles/hr * 0.25 hr = 400 vehicles. Therefore, the maximum queue length is 400 vehicles.

To calculate the average queue length in the southbound direction, we need to find the average number of vehicles queued during the entire period from 4:30 p.m. to 5:00 p.m. The average traffic flow during this period is (1600 + 1500) / 2 veh/hr/lane = 1550 veh/hr/lane. Therefore, the average number of vehicles queued during this period is (1550 - 1200) * 4 lanes * 0.5 hr = 700 vehicles. Therefore, the average queue length in the southbound direction is 700 vehicles.