Question

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)

Hint:

Webster's method is a commonly used formula to determine the optimum cycle length at signalized intersections.

Answer 1

Correct Answer: 37

The Webster’s formula for optimum cycle length is: \[ C = \frac{1.5L + 5}{1 - \sum_{i=1}^n \frac{V_i}{S_i}}. \] Where:
- \(L = 9 \, \text{seconds (lost time)}\),
- \(V_i = \text{volume of traffic for phase i}\),
- \(S_i = \text{saturation flow for phase i}\).
By applying the formula, we calculate the optimum cycle length to be: \[ \boxed{37} \, \text{seconds}. \]