$($a$)$ A signalised junction has a cycle time of $100sec-$ of which $40sec$ of

effective green time and $60sec$ of effective red time. The maximum

discharge rate is $5400vph$ during the first $40sec$ of the effective green

time, and $4500$ in the remaining $20sec.$ The arrival rates in a cycle are

given in the table below.

Assuming that at the beginning of the red time $($time $0)$ there is no

queue and that the queue process can be considered deterministic,

Draw the curves of cumulative arrivals, cumulative departures, and

queue length.

Calculate the overall average delay.

Calculate the delay of the vehicle that joins the queue at the end of

the red period.