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GATE 2019 CE (CE1) – Question 56

Traffic Engineering and Transportation Planning · Traffic studies: flow, speed, peak hour factor, accident study · 2 marks · Numerical answer

Vehicles arrive on a highway at 360/hour as a Poisson process. Find the probability of successive headway between 6 and 10 seconds, to two decimal places.

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Correct answer: .17 to .19

Explanation

Arrival rate is $\lambda=360/3600=0.1$ per second. Poisson arrivals have exponential headways: $$P(6<H<10)=e^{-0.1(6)}-e^{-0.1(10)}=0.180932.$$ Answer **0.18**.