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GATE 2017 CE (CE1) – Question 43

Traffic Engineering and Transportation Planning · Traffic signs, signal design by Webster method, intersections and interchanges · 2 marks · Multiple choice

The figure shows queue length versus time at a signalized intersection with a 96 s cycle. At $t=0$ the signal turns red. Effective green lasts 36 s and saturation discharge rate is $s$ vph. Arrivals are uniform at $v$ vph throughout the cycle. Which statement is true?

Diagram for GATE 2017 CE (CE1) question 43
  1. $v=600$ vph; average stopped delay = 30 s/vehicle.
  2. $s=1800$ vph; average stopped delay = 28.125 s/vehicle.
  3. $v=600$ vph; average stopped delay = 45 s/vehicle.
  4. $s=1200$ vph; average stopped delay = 28.125 s/vehicle.

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Correct answer: (B) $s=1800$ vph; average stopped delay = 28.125 s/vehicle.

Explanation

The queue grows to 10 vehicles over the 60 s red, so $v=10(3600)/60=600$ vph. It clears in 30 s of green, so $s-v=10(3600)/30=1200$ and $s=1800$ vph. The area under the queue curve is $\frac12(90)(10)=450$ vehicle-seconds. Arrivals per cycle are $600(96)/3600=16$, giving average delay $450/16=28.125$ seconds. Thus B.

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