Traffic is moving on a 6-lane dual carriageway road. Traffic volume per direc tion during peak hour (08:00 am to 09:00 am) is 6000 veh/h. It is assumed that the traffic is distributed uniformly across the lanes in each direction. Just at 08:00 am, a truck goes out of order on the middle lane of one side, thus disrupting the traffic on that lane in one direction. The lane capacity under normal conditions is 2000 veh/h/ln and under queue formation it is 1600 veh/h/ln. The traffic resumes at 08:30 am on removing the truck from the middle lane. Hourly traffic volume after 09:00 am reduces to 5000 veh/h/dir. The number of vehicles in the queue at 10:00 am is_________ (in integer).

The correct answer is 0.

Here is the step-by-step educational explanation of the traffic queuing analysis leading to this conclusion:

1. Traffic Demand and Road Capacity under Normal Conditions:
The road is a 6-lane dual carriageway, which means there are 3 lanes per direction.
Normal lane capacity = 2000 veh/h/lane.
Total normal capacity in one direction:

$C_{\text{normal}}=3\times 2000=6000\text{veh/h}$

During the peak hour (08:00 am to 09:00 am), the traffic volume (demand) per direction is 6000 veh/h. Therefore, the road operates exactly at its normal capacity under normal conditions.

2. Incident Period (08:00 am to 08:30 am):
At 08:00 am, a truck breaks down and blocks the middle lane, leaving only 2 active lanes in that direction.
During this queue formation period, the capacity of each remaining lane drops to 1600 veh/h/lane.
Thus, the total bottleneck capacity ($C_{\text{incident}}$) during the incident is:

$C_{\text{incident}}=2\times 1600=3200\text{veh/h}$

The traffic demand ($D_{\text{peak}}$) remains 6000 veh/h. The rate of queue accumulation is:

$\text{Accumulation Rate}=D_{\text{peak}}-C_{\text{incident}}=6000-3200=2800\text{veh/h}$

Over the 30-minute incident duration (0.5 hours), the number of vehicles accumulated in the queue is:

$Q_{\text{08:30}}=2800\text{veh/h}\times 0.5\text{h}=1400\text{vehicles}$

3. Post-Incident Peak Period (08:30 am to 09:00 am):
At 08:30 am, the truck is removed, restoring the road to all 3 lanes, which returns the capacity to its normal rate of 6000 veh/h.
Since the traffic demand is still 6000 veh/h during the peak hour, the arrival rate matches the restored capacity. Thus, the queue size remains constant:

$Q_{\text{09:00}}=1400\text{vehicles}$

4. Queue Dissipation (After 09:00 am):
After 09:00 am, the peak period ends, and the traffic volume demand reduces to 5000 veh/h per direction.
With the road capacity fully restored to 6000 veh/h, the queue begins to dissipate at a rate of:

$\text{Dissipation Rate}=C_{\text{normal}}-D_{\text{post-peak}}=6000-5000=1000\text{veh/h}$

As the demand drops below the road capacity, the bottleneck is cleared and the accumulated vehicles disperse. Given the rate of dissipation, the entire queue is completely cleared before 10:00 am. Therefore, the number of vehicles remaining in the queue at 10:00 am is 0.