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GATE 2017 CE (CE1) – Question 35

Traffic Engineering and Transportation Planning · Traffic studies: flow, speed, peak hour factor, accident study · 1 mark · Numerical answer

Vehicles arrive according to a Poisson process at 900 vehicles/hour. A gap is the time between consecutive point-vehicle arrivals. Find the probability that a gap exceeds 8 seconds, to four decimal places.

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Correct answer: 0.1276 to 0.1372

Explanation

For a Poisson arrival process, interarrival gaps have exponential distribution with rate $\lambda=900/3600=0.25$ s⁻¹. The survival probability is $P(T>t)=e^{-\lambda t}$. Hence $P(T>8)=e^{-0.25(8)}=e^{-2}=0.135335$, rounding to 0.1353. The archived accepted interval is preserved as 0.1276–0.1372.

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