Assumptions: Saturation flow rate $s=3200 \mathrm{veh} / \mathrm{hr}(1600 \mathrm{veh} / \mathrm{hr} / \mathrm{n})$. Delay is a function of the $v / c$ ratio, $X$; the green ratio, $g / C$; the cycle length, $C$; the lane group capacity, $c$; and the progression factor, PF. Lane group capacity is calculated as follows:
$$
c=s \times g / C=3200 \times 0.50=1600 \mathrm{veh} / \mathrm{hr}
$$
At LOS B threshold of $20.0 \mathrm{sec} / v e h$, the delay equation is expressed as follows:
$$
20.0=d_{1}(\mathrm{PF})+d_{2}+d_{3}
$$
where
$$
d_{1}=\frac{0.5(90)(1-0.50)^{2}}{1-(0.50 X)}
$$
MATH0081 COURSE NOTES ：
$$
X_{i}=\left(\frac{v}{c}\right){i}=\frac{v{i}}{s_{i}\left(\frac{g_{i}}{C}\right)}=\frac{v_{i} C}{s_{i} g_{i}}
$$
Therefore,
$$
X_{c}=\sum\left(\frac{v}{s}\right){c i}\left(\frac{C}{C-L}\right) $$ $$ C=\frac{L X{c}}{X_{c}-\sum_{i}\left(\frac{v}{s}\right)}
$$
and
$$
g_{i}=\frac{v_{i} C}{s_{i} X_{i}}=\left(\frac{v}{s}\right){i}\left(\frac{C}{X{i}}\right)
$$