Problem $1(12$ points$)$

An isolated intersection has a pretimed four$-$phase signal with the movements

allowed in each phase and corresponding analysis and saturation flow rates shown in

the following table. $($To simplify for calculation, the SB$/$NB maps the same values of

EB$/$NB$).$

Calculate the minimum cycle length and the effective green time for each phase.

Assume the lost time is $4$ seconds per phase and a critical intersection v$/$c of $0\mathrm{.}95$ is

desired.

Calculate the average approach delay and level of service of eastbound,

westbound, and the whole intersection $($Assume there is no initial queue$).$

Assume all the four approaches have the same width of $60ft,0\%$ grade, the

speed of vehicles approaching the intersection is $40f\frac{t}{s}.$ Calculate the yellow time,

the all$-$red times for each phase. Assume the effective crosswalk width is $6ft,$ the

maximum number of crossing pedestrians in any phase is $20,$ and the pedestrian

walking speed is $4f\frac{t}{s}.$ Calculate the minimum pedestrian green time for each

approach. Pedestrians crossing the EB or WB approach are only permitted in Phase

$4,$ while those crossing the SB or NB approach are only permitted in Phase $2.$ Then,

to accommodate the pedestrians, does the effective green time of Phase $\frac{2}{4}$ need

extension?