Here comes a signalized intersection. The cycle length is $90$ seconds, and the $\frac{g}{C}$ ratio is $0\mathrm{.}5$ ; during

the effective green interval, vehicles can depart from the intersection at a rate of $18$ vehicles per

minute. One Mustang and $11$ Escalades $(12$ vehicles in total$)$ arrive at the intersection within a span of

$90$ seconds $($so assume an arrival rate of $8ve\frac{h}{m}in$ for the first $90$ seconds and a rate of $0ve\frac{h}{m}in$

afterward$).$ The cycle begins with the effective red time, and when John arrives at the intersection,

there are already $3$ vehicles waiting in a queue. Assume that a fractional number of vehicles is

allowed.

a$)$ Determine how many seconds it will take to clear the entire queue $($measure from

beginning of the first cycle$)$ Correct answer: $140$ seconds

b$)$ What will the total delay $($in vehicles$-$second$)$ be at the approach?

Correct answer: $577\mathrm{.}5$ vehicles$-$second