Question

A traffic signal has a cycle length of 90 seconds. For the travel direction of interest: (1) Green Time = 60 seconds; (2) Red Time = 30 seconds; (3) Arrival Rate = 30 veh/min; (4) Saturation Flow (i.e. the queue discharge rate) = 1 veh/sec.

a) Calculate the total delay (veh*s) for the travel direction of interest.

b) What is the maximum queue size (veh)?

Assume road works are taking place ON THE STREET, downstream from the intersection, so that only 40 veh/min (in the direction of interest) can pass. The departure from the signalised intersection will be the arrival at the work zone section. Assume that the queue at the downstream restriction never backs-up into the intersection.

c) Calculate the maximum queue (veh) caused by the street work in one traffic signal cycle.

d) Calculate the total delay (veh*s) caused by the street work in one traffic signal cycle.

Answer 1

First Part:

Given, Arrival Rate = 30 vehicles/min or 0.5 vehicles / sec

Departure Rate (when green) = 1 veh / sec

Let's assume a cycle beginning with Red signal at t = 0.

Below is the queuing diagram:

(a) Total Delay: Area within the two curves, which is the area of the triangle:

Total Delay = 0.5 X 30 X 30 = 450 veh s

(b) Maximum queue size: Longest vertical line between the two curves, which is at t=30 s.

Maximum queue size = 15 vehicles

Second Part:

Obstruction after the signal. Now, we already have the output from the signal in the above, but will change the phase by 30 seconds for better understanding. That is at t=0, signal has turned green. With the departure rate from the obstruction being a constant of 40 veh/min i.e. (2/3) veh/sec. Below is the queuing diagram:

(c) Maximum queue Length: Will be similarly the longest vertical line between the two curves, i.e. @ t=30 s.

Maximum queue Length = 10 vehicles.

(d) Total Delay: Will again similarly be the area between the two curves.

We'll solve that in 3 parts.

(i) The triangle = 0.5 X 10 X 30 = 150 veh s

(ii) The trapezium = 0.5 X (10 + 5 ) X 30 = 225 veh s

(iii) The small triangle = 0.5 X 5 X 7.5 = 18.75 veh s

Total Delay = 393.75 veh s