Fundamentals of Transportation/Shockwaves/Homework

Homework

1. The upstream traffic flow on a road with two lanes in the relevant direction is q₁= 1800 veh/hr with freeflow speed of v₁=90 km/hr. As the result of a crash, one lane is blocked and flow is reduced to q₂ = 900 veh/hr. The density in the queue is k₂ = 70 veh/km. The value of time is $10/hour/vehicle

A. What is the shockwave speed (v_w)?

B. If this continues for 1 hour, before the lane is cleared, how many vehicles long will the queue be?

C. How much did this crash cost society in terms of delay (travel time in excess of freeflow travel time)?

D. If a freeway service patrol (tow truck service) could clear the crash in 30 minutes instead of an hour, how much should society be willing to pay for that service?

E. If a variable message sign placed 2 km upstream of the crash site instantly (at the moment of the crash) advises travelers about a diversion to a frontage road 1 km upstream of the crash site, how valuable is the freeway service patrol (how much should society be willing to pay under these circumstances)?

2. A fixed-time ramp meter with unlimited storage space can serve 1 vehicle every 5 seconds. Vehicles approach the back of the ramp queue at 80 km/hr at a rate of 1 vehicle every 4 seconds. The density in the queue is 275 veh/km.

A. What is the wave speed?

B. What is the rate at which the queue grows, in units of vehicles per hour (q)?