Traffic flow on a section of a two-lane highway can be described by the Greenshields model, with a mean free speed of 55 mph and a jam density of 145 veh/mi/ln. At the time when the flow was 90% of the capacity of the highway, a large dump truck loaded with heavy industrial machinery from an adjacent construction site joins the traffic stream and travels at a speed of 15 mi/hr for a length of 3.5 mi along the upgrade before turning off onto a dump site. Due to the relatively high flow in the opposite direction, it is impossible for any car to pass the truck. Determine how many vehicles will be in the platoon behind the truck by the time the truck leaves the highway.

Question

What will be an ideal response?

Answer 1

Knowing the traffic conditions can be described using Greenshields’ model

allows use of Equation 6.53 which relates speed of the shockwave to the densities

associated with flow before and during the blockage.



The growth rate of the platoon is 15 mi/h forward and 3.8 mi/h backward, which

is a total of 18.8 mi/h. The truck is on the highway for 3.5 mi / 15 mph = 0.233 hr

The platoon length at the end of the duration is (18.8 mi/h)(0.233 hr) = 4.38 mi

The number of vehicles in the platoon is (4.38 mi)(105.5 veh/mi) = 462 vehicles.