Question $4)$

A traffic engineer is evaluating the efficiency of the greenband wave in a coordinated signal corridor along a $1\mathrm{.}5-$kilometer section of road. The corridor consists of four signalized intersections spaced $500$ meters apart. The signals are synchronized with a cycle length of $120$ seconds. The green time at each signal is $45$ seconds, and the offset between consecutive signals is $25$ seconds.

The posted speed limit along the corridor is $\backslash (60\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ),$ and traffic flows freely at this speed. During peak hours, the traffic volumes at each intersection are as follows:

a$)$ Draw a time$-$space diagram showing the progression of the greenband wave for the entire corridor, assuming all vehicles travel at the speed limit$.$

b$)$ Calculate the width of the greenband $($in seconds$)$ at each intersection. $($Answer $\backslash (=40\backslash$mathrm$\{$~s$\},35\backslash$mathrm$\{$~s$\},30\backslash$mathrm$\{$~s$\}\backslash ))$

c$)$ Determine the efficiency of the greenband wave at each intersection by calculating the percentage of the cycle length that vehicles can travel through the intersection without stopping $($greenband width divided by cycle length$).($Answer $\backslash (=33\backslash \%,29\backslash \%,25\backslash \%\backslash ))$