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

ID: 1822542 • Letter: A

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 a,. Assume D/D/1 queuing to determine time of queue dissipation, longest queue length, total delay, average delay per vehicle, and longest wait of any vehicle.

Explanation / Answer

We will be using deterministic queuing

Q1 = 2900 veh/h

Capacity = 4000 veh/h

From 8 am to 8:12 am

Vehicles arrived = 2900 * 12/60 = 580 vehicles

vehicles departed = 0

Length of queue = 580

From 8:12 am to 8:31 Am

Vehicles arrived = 2900 * (19)/60 = 918

Vehicles departed = 2000* 19/60 = 633

Queue length = 580 + 918 - 633 = 865

From 8:31 am onwards.

Capacity has increased to 4000 veh/h

The flow will be equal to capacity till queue is cleared.

Time taken to clear queue is

(4000 - 2900)*t = 865

t = 865/(4000 - 2900) * 60 = 47.18 min

The queue will dissipate at 8:31 + 47.18 i.e, 9:28 AM

Longest queue length happens at 8:31 Am i.e, 865 vehicles

if we take average length of vehicle as 5.5 m queue lenght = 865 *5.5 = 4757.5 metre