GATE 2019 CE (CE2) – Question 54
Uniform arrival and service rates at a signalized approach are 20 and 50 vehicles/min respectively. Red time is 30 s, effective green 30 s and cycle 60 s. Initially no vehicles are queued. Find average delay per vehicle approaching in one cycle (s), to two decimal places.
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Correct answer: 12 to 13
Explanation
Red builds a queue of $20(0.5)=10$ vehicles. During green it clears at $50-20=30$ vehicles/min, taking 1/3 min. Queue–time area is $\tfrac12(10)(0.5+1/3)=4.16667$ vehicle-min. Divide by 20 arrivals per cycle: 0.208333 min, or **12.50 s/vehicle**.