Problem $6\mathrm{.}3(7$ Points$)$

Textbook Problem $\backslash$#$8-16,$ page $444($Garber $\backslash$& Hoel, Traffic and Highway Engineering, $5$th Ed$.).$

Determine the optimal phasing plan, cycle length, and the length of green time for each phase based on the traffic volumes and PHF data presented in the textbook. Two phasing options and the corresponding saturation flow rate for each movement per phase is presented below. The saturation flow rates assume that the North$-$South approaches have two lanes each $($no turn lanes$)$ and the East$-$West approaches have two lanes each plus a dedicated left turn lane. The optimal phasing plan is the plan that provides the lowest total $\backslash (\backslash$mathrm$\{$v$\}/\backslash$mathrm$\{$s$\}\backslash )$ ratio for the intersection with the fewest phases. Assume a lost time of $5$ seconds per phase.

Option A: Three$-$Phase