Studies have shown that the traffic flow on a two-lane road adjacent to a school

Question

Studies have shown that the traffic flow on a two-lane road adjacent to a school eenshields model. A length of 0.5 mi adjacent to a school is 6) (2 0 pts) can be described by the G described as a school zone (see Figure below). The school zone operates for only 20 min. Data collected at the site when the school zone is in operation are given below Section A 0.5 mile Section C Section B School Zone Determine the speed of the shock waves AB and BC. Also determine both the length of the queue after the 20 min. period and the time it will take the queue to dissipate after the 20 min period. qA (one direction) 1750 veh/h ua 35 mi/h gB (one direction) 1543 veh/h ub 18 mi/h gc(one direction) =1714 veh/h uc-30 mi/h

Explanation / Answer

Expression for shock wave is given as : Ratio of change in flow to change in density.

Given are the q ( flow ) and u ( speed ) values, and we know that k (density ) = q / v. (By Greenshield's model, linear relarionship)

So,

Speed of shock wave AB = ( 1543 - 1750 ) / ( ( 1543/18 ) - ( 1750/35 ) ) = 5.79 mi/h (backward direction)

Speed of shock wave BC = ( 1714 - 1543 ) / ( ( 1714/30 ) - ( 1543/18 ) ) = 5.98 mi/h (backward direction)

Now, the queue will be behind the school zone.

Hence, queue length, N = (1750/35) * ( 35 - ( 5.79 ) ) * ( 20/60 ) = 1750 * 29.21 / ( 3 * 35 ) = 486.83 or 487 vehicles

This queue will dissipate, when zone B stops operating, hence,

487 = (1543/18) * ( 18 - 5.98 ) * t

On solving for t, we get, t = 0.472 hours or t = 28.3 min.

Hence, it takes 28.3 minutes to dissipate the queue.

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