An approach at a pre$-$timed signalized intersection has a saturation flow of $2000ve\frac{h}{h}$ and is allocated $35$ seconds of effective green in a $60-$second signal cycle. If the flow at an approach is $800$ vph $,$ calculate the following properties of the approach based on D$/$D$/1$ queuing model: $(7$pts$)$

Time to Queue dissipation after the start of effective green time $(t_c)$

Proportion of cycle with queue $(P_q)$

Proportion of vehicles stopped $(P_s)$

Maximum no$.$ of vehicles in queue $(Q_{\text{m}\text{a}\text{x}})$

Total vehicle delay per cycle $(D_t)$

Average vehicle delay per cycle $($d avg$)$

Maximum delay of any vehicle $(d_{\text{m}\text{a}\text{x}})$