an incident occurs on a freeway that has a capacity in the northbound direction,

Question

an incident occurs on a freeway that has a capacity in the northbound direction, before the incident, of 4000 veh/h and a constant flow of 2900 veh/h during the morning commute. ( no adjustments to traffic flow result from the incident) at 8:00 am a traffic accident closes the freeway to all traffic. at 8:12 am the freeway is partially opened with a capacity of 2000 veh/h. Finally, the wreckage is removed, and the freeway is restored to full capacity (4000 veh/h) at 8:31 am.

a.) Draw a queue diagram representing the traffic flow starting at 8 am

b.) Determine the time of queue dissipation

c.) Determine the longest queue length

d.) Determine the longest wait of any vehicle

e.) Determine the total delay

f.) Determine the average delay per vehicle

Explanation / Answer

A) At 8:00 am a traffic accident closes the freeway to all traffic and queue of vehicle will start forming with rate=2900 veh/h;

queue diagram representing the traffic flow

starting at 8 am will be straight line passing through origin (at 8 it will be 0.) with slope = rate of que formation=2900 veh/h for 12 min

Area1 =580 vehicle;

at 8:12 am the freeway is partially opened with a capacity of 2000 veh/h;

queue of vehicle will start forming with rate=900 veh/h; till 8:31

Area2 =285 vehicle;

When, the wreckage is removed, and the freeway is restored to full capacity (4000 veh/h) at 8:31 am.

Rate of queue dissipation = 1100 veh/h;

the time of queue dissipation= 31+(580+285)/rate= 31+47 min=78 min

(C)the longest queue length =580+285=865

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