The Hong Kong Polytechnic University

Department of Civil and Environmental Engineering

CSE40407 DESIGN OF TRANSPORT INFRASTRUCTURE

Tutorial 3 Traffic Signal

From last week…

In Tutorial 2, we examined the performance of the following roundabout under the given design
flow.

Since we were told that, generally speaking, roundabout and signal junction have a similar range of
junction capacity. Let’s try to see what happens if we try to use a signal junction instead. To the sake
of fair comparison, we still assume all 4 approaches are dual 2-lane carriageways.

CSE40407 Tutorial 3 – Traffic Signal 1

Major steps in Traffic Signal Design
Step 1. Stage Diagram
Step 2. Determine cycle length
Step 3. Green allocation
Step 4. Analyze performance

Junction Geometry and Design Flow

- Both the E-W and N-S approaches are dual 2-lane carriageway, same as roundabout tutorial
- Design flow is already in pcu/hr, same setting as roundabout tutorial

150 300 150

200
600
300

150
700
150

200 400 200

Stage Diagram
For simplicity, let’s assume a 2-stage plan as follows

Stage I Stage II

About stage plan

1. A ‘stage’ denotes the period of time that the signal
display remains unchanged. All movements
(arrows) in that stage enjoy the same (effective)
green time and are moving together.
2. Take Stage I as an example. The through (TH)
movements can use both lanes, but the LT (or RT)
movement should use the nearside (farside) lane
only, to avoid conflict. The actual lane marking
should be consistent to the stage plan, see figure
on the right for lane marking corresponding to
this example.

CSE40407 Tutorial 3 – Traffic Signal 2

3. In the stage plan, it is customary that protected movements (movements that would not see conflict
from other vehicle streams or pedestrians, or simply being the movements that have higher priority in case
conflict happens) are denoted by solid lines, while permitted movements (lower priority) are
denoted by dotted lines.
4. It is ok to use curved arrows to represent turning movements, straight line arrows are used here
simply because of the limitation of MS Word.
5. Feel free to develop a 3-stage or even 4-stage plan that involves less permitted movements
(improve safety). We use a simple 2-stage plan for the sake of preliminary design and discussion
in this tutorial.
See below for examples of possible 3-stage plans. It is left to students as an exercise to verify that
with more stages, there are more lost time per cycle due to phase change, so that the junction
operates less efficiently.

Stage I Stage II Stage III

Stage I Stage II Stage III

Both of these 3-stage plans allow for protected RT in the eastbound and westbound directions.
However, the second example involves the use of exclusive RT lane, i.e. the farside lane can be
used for RT only, the lane marking in the diagram in p.2 needs to change accordingly as well.

CSE40407 Tutorial 3 – Traffic Signal 3

Signal Calculation Sheet
A blank signal calculation sheet is available from Blackboard. You are expected to manually input
the expressions for saturation flow and other adjustments according to the expressions in TPDM.

First, we input the stage plan and design flow (pcu/hr).

For example, for the Eastbound approach has the design flow: .
According to the stage plan, LT flow is using the nearside lane only, RT flow is using the farside lane
only, and the TH movement is distributed over the 2 avaialble lanes.
- We assume1 that the 600veh is distributed equally across the two lanes.
- Thus, the TH + LT lane has a design flow of 200 + 600 × 0.5 = 500𝑣𝑝ℎ, and the TH + RT lane
has a design flow of 300 + 600 × 0.5 = 600 𝑣𝑝ℎ.

Since the given design flow in this question is already in pcu/hr, no conversion is necessary.

1Other assumptions of split that is consistent to the natural ways the drivers are picking a lane is considered
reasonable, such as 60:40, 40:60. In case of 3 lanes, a flow split like 33:34:33 or 30:40:30 is acceptable. A ‘natural’
distribution would result in comparable y-values in Col 7 over different lanes on the same approach.

CSE40407 Tutorial 3 – Traffic Signal 4

Then, we move on to computation of Saturated Flow.
Take note of the following expressions for Saturated Flows

For simplicity, assume that the junction is located at level ground.

- We first compute the Saturation flow as if it is a straight-ahead lane first (Col 4).
- And then do adjustments for shared lane and/or opposing movements (results in Col 6)
- For turning movements, we need to know the turning radius. For this exercise, let’s assume 𝒓 =
𝟕. 𝟓𝒎 for left turn, 𝒓 = 𝟏𝟓𝒎 for right turn.

To do: Insert the missing values in Col 4, 5 and 6 in the last page of this handout.

CSE40407 Tutorial 3 – Traffic Signal 5

Next, compute the 𝒚 ratio, cycle time and the effective green allocation.
- 𝑦 = 𝑞/𝑆 where 𝑞 is the design flow (col 2) and 𝑆 is the saturation flow (col 6)
- For each stage, pick the lane that has a highest 𝑦 (i.e. ‘busier’) to be the 𝑦 value of that stage (col
8)
- Since this is a 2-stage plan. Under typical assumption of 4 sec lost time (𝑙) per stage change, the
total lost time is 𝐿 = 2 × 𝑙 = 8𝑠𝑒𝑐 (col 10)
- Compute cycle time using Webster’s formula (box 11 at the bottom), round up to the next 5 sec,
which would be 40 seconds
- Allocate effective green to each stage by distributing (𝑐 − 𝐿) according to 𝑦 value, where 𝑐 − 𝐿
represents the amount of time that can be used by traffic in a cycle. (col 19)

To do: Insert the missing values in Col 7 to 19 in the last page of this handout.

(numerical ans for checking)

Finally, we examine the junction performance.

Comment: This junction has a reserve capacity of 51.2% (box 15), which is satisfactory.

According to TPDM, we should provide a reserve capacity of 25% for new junctions. Or if we refer
to the TIA guideline, we would like to achieve a reserve capacity of 15%.

CSE40407 Tutorial 3 – Traffic Signal 6

Discussion: Roundabout vs Traffic Signal
Capacity consideration
• Roundabout (p.1): All entries have DFC well below the acceptable threshold of 85%.
• Traffic Signal: Reserve capacity = 51.2%, which is well below the acceptable threshold as well.
In that case, we can conclude that both roundabout design and traffic signal can provide
sufficient capacity for this junction.

Apart from capacity, what are the other criteria that one should consider while choosing
between roundabout and signal junction?

Degree of saturation
While reserve capacity (RC) gives an indication of the overall performance, degree of saturation (col
16) provides some insight about how busy each lane may get. The degree of saturation is analogous
to the notion of volume-to-capacity ratio.
𝑔
- Recall that the capacity of an approach, 𝑄 = 𝑆 × 𝐶 , which indicates the ‘capability’ of an approach
in discharging vehicles.
𝑑𝑒𝑠𝑖𝑔𝑛 𝑓𝑙𝑜𝑤 𝐶𝑜𝑙 2 𝐶𝑜𝑙 2 𝐶𝑜𝑙 16
- Volume-to-capacity is essentially 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦
= 𝐶𝑜𝑙 19 = 𝐶𝑜𝑙 6 × 𝐶𝑜𝑙 19
(𝐶𝑜𝑙 6)×
𝐶𝑜𝑙 16

CSE40407 Tutorial 3 – Traffic Signal 7

Extension 1 [if time permits] – 3-stage plan
For this junction, if the following 3-stage plan is adopted, it makes the junction performance worse,
with a reserve capacity of only 2.91% (not acceptable)

Original 2-stage plan

Stage I Stage II
New 3-stage plan

• Change from permitted turn to protected turn: small increase in saturation flow (Sat flow eqt)
• Increase no. of stages => more lost time per cycle
• When the RT volume is becoming high, RT vehicles waiting in the middle of the junction (with
or without RT pocket) may cause safety problems and excessive delay => consider RT protection.

CSE40407 Tutorial 3 – Traffic Signal 8

Extension 2 [if time permits] – heavy RT
Recall in the roundabout tutorial that, we examined a case of heavy RT volume and found the
performance is still satisfactory:

If we redo the signal calculation using the same 2-stage plan,

we see that the junction performance is not very satisfactory,
the reserve capacity is only 14.63%.

CSE40407 Tutorial 3 – Traffic Signal 9

In fact, the above is not a very good example.
- In view of the very heavy RT, we should give the entire farside lane for RT vehicles (note the
new drawing in the “movement/ phase” columns), grouping all TH + LT on the nearside lane
only. (See lecture notes p.58).

- Note that although the RT vehicles are using the entire lane now, it is still a permitted turn
(dotted lines) since the RT vehicles would still experience conflicts from other TH traffic. [need
to update the lane marking!!!]

Notice that there is an improvement in RC in this scenario and the RC is now satisfactory.

CSE40407 Tutorial 3 – Traffic Signal 10

 Summary

- Practiced manual signal calculation following TPDM requirements through the use of a signal
calculation sheet
o Development of stage plan,
o Distribution of flow across lanes, pcu adjustment,
o Saturation flow calculation (nearside/ farside, protected/ permitted turn, proportion
of turning movement in a lane, gradient)
o Cycle time calculation and effective green allocation
o Performance analysis: RC and degree of saturation

- Signal junction vs roundabout ?

Capacity? Safety? Land intake? Pedestrian? Visibility ⇔ site constraint?

CSE40407 Tutorial 3 – Traffic Signal 11

Signal Calculation Sheet (for 2-stage plan)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (16) (19) (20)
𝑔=
Lane Turning Design Gradient Sat Propn. of Rev. Sat. greater =∑ - Selected 𝑦 deg. Sat =
Movement/Phase Stage y=(2)/(6) =∑ (𝑐 − (2) (16)
width radii flow effect Flow turning Flow y 1) c 𝑌 ×
(6) (19)
𝐿)
(m) (m) (pcu/hr) (pcu/hr) (pcu/hr) (sec) (sec)
1
3.65 7.5 500 0.574

3.65 15 600 0.702

3.65 15 500 0.574

3.65 7.5 500 0.564

2
3.65 7.5 300 1980 0.5 1800 0.167 0.513

3.65 15 300 2120 0.5 1800 0.167 0.513

0.222
3.65 7.5 400 1980 0.5 1800 0.222 0.684

3.65 15 400 2120 0.5 1800 0.222 0.684

1.5𝐿+5
(11) 𝐶𝑜 =
1−𝑌
𝐿
(12) 𝐶𝑚 = 18.00
1−𝑌
(13) 𝑌𝑢𝑙𝑡 = 0.9 − 0.0075𝐿 0.84
𝑌𝑢𝑙𝑡 −𝑌
(14) 𝑅. 𝐶.𝑢𝑙𝑡 = × 100% 51.20%
𝑌
0.9𝐿
(15) 𝐶𝑝 = 20.90
0.9−𝑌
(16) Assigned c
(round up to nearest 5 sec)
𝐿
(17) 𝑌𝑚𝑎𝑥 = 1 − 0.80
𝐶
0.9𝑌𝑚𝑎𝑥 −𝑌
(18) 𝑅. 𝐶.𝑐 = × 100% 29.60%
𝑌

CSE40407 Tutorial 3 – Traffic Signal 12