An intersection is located in an area with no slope. Due to the heavy traffic observed in the

intersection, especially during the morning and evening peak hours, the municipality has decided

to signalize the intersection. Two phases are considered for the signal, where phase $1$ is dedicated

to the major street on the East$-$West bound $($including through, right turn, and left turn

movements$)$ and phase $2$ is dedicated to the minor street on the North$-$South bound $($including

through, right turn, and left turn movements$).$ The street widths in the E$-$W and N$-$S directions

are respectively measured at $50$ and $30$ feet and $\{$:$L_2=30),$ as shown in the figure below.

The speed and time headway values of two samples of vehicles are measured; one sample in the

E$-$W direction and the other sample in the N$-$S direction. In addition, the speed of a pedestrian

sample is measured. The signal should be designed for the $80$th percentile speed of the two vehicle

samples and the $50$th percentile speed of the pedestrian sample. The values can be found in the

table below. It is also observed that the length of a typical vehicle is $16ft.$

$($a$)$ Design the two$-$phase signal only for the vehicles for a cycle length equal to $120$ seconds, and

minimum green interval of $25$ seconds for the minor street $(t_r=1(s)).$ DRAW THE TWO PHASES.

$($b$)$ Design the signal by including the pedestrian. DRAW THE PHASES.

$($c$)$ Calculate the intersection capacity in both directions.