$8\mathrm{.}4.$ A ramp meter operates during the morning peak period. Ramp meter cycles vary with time as shown in the table below. The metering scheme allows one vehicle per cycle to pass the signal, so that $($for instance$)$ a $6$ s cycle corresponds to a service rate of one vehicle every $6s$ or $600$ vehicles per hour. The table below gives the number of vehicles demanding service on the ramp during particular time intervals, the cumulative demand for the ramp for the morning peak, and the ramp meter cycle for each interval. Using a queuing diagram determine: $(a)$ the time the queue on the ramp begins and ends, $($b$)$ the maximum number of vehicles in the ramp queue, and $($c$)$ the total delay due to queuing on the ramp.

$\backslash$table$[[$Time period,$10-$min,Cumulative,$],[$volume$,$volume,Meter cycle,s$,],[6$:$30-6$:$40,80,80,6],[6$:$40-6$:$50,90,170,10],[6$:$50-7$:$00,100,270,12],[7$:$00-7$:$10,60,330,10],[7$:$10-7$:$20,70,400,6],[7$:$20-7$:$30,50,450,6]]$