Designing a signal means answering one question: how long should the cycle be, and how should it be split between the roads?
There are four established ways to answer it. This post covers the list, works through the trial cycle method in full, and then handles pedestrian timing — which every signal design must accommodate.
The Four Methods
- Trial cycle method
- Approximate method
- Webster method
- IRC method
They differ in how they arrive at the cycle time. The trial cycle method guesses and checks. The approximate method uses a simplified procedure. Webster’s method calculates an optimum from delay theory. The IRC method combines approaches and applies a check.
Webster and IRC are covered in their own posts. This one deals with the first two, plus pedestrian movement.
The Trial Cycle Method
The name gives the game away — this is a hit and trial method. You assume a cycle time, work through the consequences, and see whether the answer matches your assumption.
Step 1 — Count the Traffic
15 minute counts nA and nB are taken on road A and road B during the design peak hour flow.
Note that the counts are taken during the peak, because a signal that works at the peak will work at quieter times, while the reverse is not true.
Step 2 — Assume a Cycle Time
Assume a cycle time C. This is the guess that the method will later test.
Step 3 — Find Vehicles Passing per Cycle
Convert the 15-minute count into the number of vehicles arriving in one cycle:
xA = [ nA / (15 × 60) ] × C
xB = [ nB / (15 × 60) ] × C
The logic is simple. 15 × 60 = 900 seconds, so nA/900 is the arrival rate in vehicles per second. Multiply by the cycle length in seconds and you get vehicles per cycle.
Step 4 — Convert Vehicles into Green Time
The average time required for one vehicle to cross the intersection equals the time headway, generally assumed as 2.5 seconds.
GA = 2.5 xA
GB = 2.5 xB
If xA vehicles must get through and each takes 2.5 seconds, the green time needed is simply the product.
Step 5 — Add Everything Up
The total cycle time is the sum of all the periods in it:
C1 = GA + AA + GB + AB + Pedestrian time
where AA and AB are the amber periods for the two roads.
Step 6 — Compare and Repeat
If the calculated cycle time C1 equals the assumed cycle time C, then the calculated value is taken as the actual or design cycle time.
If it does not match, you assume a new value and go round again. Hence “trial”.
Why the Method Converges
It is worth seeing why this works rather than treating it as blind guessing.
Assume too short a cycle, and few vehicles arrive per cycle — but the fixed overheads of amber and pedestrian time still have to be added, so the computed cycle comes out longer than assumed. Assume too long a cycle, and the many arriving vehicles need so much green that the computed value overshoots differently. Somewhere between the two lies the value where assumption and calculation agree, and iterating steadily approaches it.
The Approximate Method
The approximate method is applied to a two-phase signal along with a pedestrian signal, at a junction of two roads of widths W1 and W2.
It is quicker than the trial cycle method because it does not iterate. Its main role, as we shall see in the IRC method, is to produce an initial timing that can then be checked by a more rigorous approach.
Pedestrian Movement
Pedestrians are not an afterthought in signal design. A crossing pedestrian occupies the junction just as a vehicle does, and needs enough time to get across at walking speed.
The Three Pedestrian Periods
| Symbol | Meaning |
|---|---|
| DW | Do not walk time |
| W | Walk time |
| CI | Clearance interval |
Do Not Walk Periods
A pedestrian must not walk across a road while vehicles on that road have the green. So the do-not-walk period for one crossing equals the green plus amber of the traffic movement it conflicts with:
DW1 = R2 = G1 + A1
DW2 = R1 = G2 + A2
Clearance Interval
The clearance interval is the time a pedestrian needs to finish crossing, calculated from the road width and walking speed:
CI1 = W1 / 1.2 and CI2 = W2 / 1.2
| Symbol | Meaning | Unit |
|---|---|---|
| W1, W2 | Width of road 1 and road 2 | metres |
| 1.2 | Speed of the pedestrian | m/sec |
This is nothing more than distance divided by speed. The 1.2 m/sec figure is the standard pedestrian design walking speed, the same value used elsewhere in traffic engineering.
Watch the notation carefully. W is used for two different things here — W1 and W2 in the clearance formula are road widths in metres, while W on its own means walk time in seconds. Read each formula in context.
Walk Periods
The walk period is what remains of the red period after the clearance interval has been set aside:
Walk period 1 = R1 − CI1
Walk period 2 = R2 − CI2
Reading the Logic
The whole scheme rests on one sensible idea: a pedestrian who starts crossing must be able to finish before vehicles are released.
So the red period available to a pedestrian is split in two. During the first part they may start walking. During the last part — the clearance interval — nobody new may start, but anyone already on the road has time to complete the crossing. The clearance interval is exactly long enough for someone who stepped off the kerb at the last permitted moment to reach the far side at 1.2 m/sec.
This is the pedestrian equivalent of the amber light for vehicles, and it exists for exactly the same reason.
Formula Summary
| Quantity | Expression |
|---|---|
| Vehicles per cycle, road A | xA = [nA/(15 × 60)] × C |
| Vehicles per cycle, road B | xB = [nB/(15 × 60)] × C |
| Green time | GA = 2.5 xA, GB = 2.5 xB |
| Cycle time | C1 = GA + AA + GB + AB + pedestrian time |
| Do not walk period | DW1 = R2 = G1 + A1 |
| Clearance interval | CI = road width / 1.2 |
| Walk period | W = R − CI |
| Time headway assumed | 2.5 sec |
| Pedestrian speed | 1.2 m/sec |
Quick Revision Notes
- Four signal design methods: trial cycle, approximate, Webster and IRC.
- Trial cycle method uses 15 minute counts during the design peak hour.
- Vehicles per cycle = (count / 900) × assumed cycle time.
- Average time for one vehicle to cross = time headway = 2.5 sec.
- Green time = 2.5 × vehicles per cycle.
- Cycle time = green + amber for both roads, plus pedestrian time.
- It is a hit and trial method: the answer is accepted when the calculated cycle equals the assumed cycle.
- The approximate method applies to a two-phase signal with a pedestrian signal.
- Pedestrian terms: DW do not walk, W walk, CI clearance interval.
- DW for one crossing equals the green plus amber of the conflicting movement.
- Clearance interval = road width / 1.2, with 1.2 m/sec as the pedestrian speed.
- Walk period = red period minus clearance interval.
Mistakes Students Commonly Make
- Using 15 instead of 900 in the denominator. The count is over 15 minutes, which is 15 × 60 seconds.
- Forgetting to add pedestrian time when totalling the cycle.
- Omitting the amber periods from the cycle total.
- Confusing the two meanings of W — road width in metres in the clearance formula, walk time in seconds elsewhere.
- Multiplying road width by 1.2 instead of dividing. Clearance interval is distance over speed.
- Adding the clearance interval to the red period instead of subtracting it to get the walk period.
- Accepting the first computed cycle without checking it against the assumed value. The method requires them to agree.
Conclusion
The trial cycle method is the most intuitive of the four design approaches — count the traffic, guess a cycle, work out how much green each road needs at 2.5 seconds per vehicle, add the ambers and the pedestrian time, and check whether your guess was right. Pedestrian timing then layers on top, splitting each red period into a walk portion and a clearance portion so that anyone who starts crossing can finish safely. Between them these two ideas cover the practical half of signal design; Webster’s method supplies the theoretical half.
Frequently Asked Questions
What are the four methods of signal design?
The trial cycle method, the approximate method, the Webster method and the IRC method.
Why is the trial cycle method called a hit and trial method?
Because a cycle time is assumed at the start, and the calculation is accepted only when the computed cycle time comes out equal to the assumed value. Otherwise a new value is assumed and the process repeated.
Over what period are the counts taken?
15 minutes, on each road, during the design peak hour flow.
How is the number of vehicles per cycle found?
By multiplying the arrival rate by the cycle time: x = [n/(15 × 60)] × C, where n is the 15 minute count and C is the assumed cycle in seconds.
What time headway is assumed?
2.5 seconds, taken as the average time for one vehicle to cross the intersection.
How is green time calculated?
Green time equals 2.5 multiplied by the number of vehicles passing in one cycle on that road.
What makes up the total cycle time?
The green and amber periods for both roads, plus the pedestrian time.
What pedestrian walking speed is used in design?
1.2 metres per second.
How is the pedestrian clearance interval calculated?
By dividing the road width in metres by the pedestrian speed of 1.2 m/sec.
What is the purpose of the clearance interval?
It ensures that a pedestrian who begins crossing at the last permitted moment can reach the far side before vehicles are released, in the same way that the amber light clears vehicles from the junction.
How is the pedestrian walk period found?
By subtracting the clearance interval from the corresponding red period.