Question

4 An approach to a pretimed signal has 30 seconds of effective red, and D/D/1 queuing holds. The total delay at the approach is 83.33 veh-s/cycle and the saturation flow rate is 1000 veh/h. If the capacity of the approach equals the number of arrivals per cycle, determine the approach flow rate and cycle length.

Answer 1

Following are the responses to the given question:

Step-by-step explanation:

Effective red duration is applied each cycle r=30 second D/D/1 queuing

In total, its approach delay is 83.33 sec vehicle per cycle

Flow rate(s) of saturated = 1,000 vehicles each hour

Total vehicle delay per cycle
`= (v * 30^2)/(2(1-(v)/(0.2778)))`

`\to (v* 30^2)/(2(1-(v)/(0.2778)))= 83.33\\\\\to 900v=166.66-599.928v\\\\\to v=0.111 (veh)/(sec)\\\\`

The flow rate for such total approach is 0.111 per second.

The overall flow velocity of the approach is 400 cars per hour

The approach capacity refers to the number of arrivals per cycle.

Environmentally friendly time ratio to cycle length:

`,(g)/(C) \ is = (400)/(1000)=0.4\\\\r= c-g\\\\30\ sec =C - 0.4 C\\\\C=50 \ sec`