GATE 2022 CE (CE2) – Question 65

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

The lane configuration with lane volumes in vehicles per hour of a four-arm signalized intersection is shown in the figure. There are only two phases: the first phase is for the East-West and the West-East through movements, and the second phase is for the North-South and the South-North through movements. There are no turning movements. Assume that the saturation flow is 1800 vehicles per hour per lane for each lane and the total lost time for the first and the second phases together is 9 seconds. The optimum cycle length (in seconds), as per the Webster’s method, is ____________. (round off to the nearest integer)

Four-arm intersection showing lane flows and two signal phases. See the attached source image.

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Correct answer: 37

Explanation

For each phase use its highest lane flow ratio. East–west critical flow is 504 vehicles/h/lane and north–south is 396, so $Y=504/1800+396/1800=0.5$.

Webster’s optimum cycle is $C_0=(1.5L+5)/(1-Y)=(1.5(9)+5)/(1-0.5)=\mathbf{37}$ s. Summing parallel lanes would overstate the critical ratio.