1. Chapter 20: Basic principles of intersection signalization
Chapter objectives: By the end of this chapter the student will be able to:
Explain the meanings of the terms related to signalized intersections
Explain the relationship among discharge headway, saturation flow, lost times, and capacity
Explain the “critical lane” and “time budget” concepts
Model left-turn vehicles in signal timing
State the definitions of various delays taking place at signalized intersections
Graph the relation between delay, waiting time, and queue length
Explain three delay scenarios (uniform)
Explain the components of Webster’s delay model and use it to estimate delay
Explain the concept behind the modeling of random and overflow delay
Know inconsistencies existing between stochastic and overflow delay models
Chapter 20

2. Discharge headways, saturation flow rates, and lost times
Four critical aspects of signalized intersection operation discussed in this chapter
Discharge headways, saturation flow rates, and lost times
Allocation of time and the critical lane concept
The concept of left-turn equivalency
Delay as a measure of service quality
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3. 20.1.1 Components of a Signal Cycle
Cycle length
Phase
Interval
Change interval
All-red interval (clearance interval)
Controller
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4. Signal timing with a pedestrian signal: Example
Interval
Pine St.
Oak St. %
Veh.
Ped. 1
G-26
W-20
R-31
DW-31
36.4 2
FDW-6
10.9 3
Y-3.5
DW-29
6.4 4
R-25.5
AR 2.7 5
G-19
W-8
14.5 6
FDW-11
20.0 7
Y-3
DW-5
5.5 8
R-2
AR 3.6
Cycle length = 55 seconds
Chapter 20

5. 20. 1. 2 Signal operation modes and left-turn treatments & 20. 1
Signal operation modes and left-turn treatments & Left-turn treatments
Operation modes:
Pretimed (fixed) operation
Semi-actuated operation
Full-actuated operation
Master controller, computer control, adaptive traffic control systems for coordinated systems
Left-turn treatments:
Permitted left turns
Protected left turns
Protected/permitted (compound) or permitted/protected left turns
Chapter 20

6. Factors affecting the permitted LT movement
LT flow rate
Opposing flow rate
Number of opposing lanes
Whether LTs flow from an exclusive LT lane or from a shared lane
Details of the signal timing
Chapter 20

7. CFI (Continuous Flow Intersection)
Bangerter Highway & 3500 South
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8. DDI (Diverging Diamond Interchange)
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9. Four basic mechanisms for building an analytic model or description of a signalized intersection
Discharge headways at a signalized intersection
The “critical lane” and “time budget” concepts
The effects of LT vehicles
Delay and other MOEs (like queue size and the number of stops)
Chapter 20

10. 20.2 Discharge headways, saturation flow, lost times, and capacity
Start-up lost time
Effective green h
Vehicles in queue
Total lost time
Saturation flow rate
Clearance lost time e
Startup lost time
Extension of green Gi
Capacity yi
ari
Cycle length
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11. Sample problem, p. 467 First approach: Second approach: Eq. 20-6
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12. 20.2.6 Saturation flow rates from a nationwide survey
Chapter 20

13. 20.3 The “critical lane” and “time budget” concepts
Each phase has one and only one critical lane (the most intense traffic demand). If you have a 2-phase signal, then you have two critical lanes.
345
Total loss in one hour
Total effective green in one hour
100 75
Max. sum of critical traffic demand; this is the total demand that the intersection can handle.
450
N = No. of phases; tL = Lost time in seconds per phase; C = Cycle length, sec; h = saturation headway, sec/veh
Chapter 20

14. 20.3.2 Finding an Appropriate Cycle Length
Desirable cycle length, incorporating PHF and the desired level of v/c Eq Eq
Doesn’t this look like the Webster model?
The benefit of longer cycle length tapers around 90 to 100 seconds. This is one reason why shorter cycle lengths are better. N = # of phases. Larger N, more lost time, lower Vc.
Chapter 20

15. Webster’s optimal cycle length model
C0 = optimal cycle length for minimum delay, sec
L = Total lost time per cycle, sec
Sum (v/s)i = Sum of v/s ratios for critical lanes
Delay is not so sensitive for a certain range of cycle length  This is the reason why we can round up the cycle length to, say, a multiple of 5 seconds.
Chapter 20

16. 20.3.2 Finding an Appropriate Cycle Length
Desirable cycle length, Cdes
Marginal gain in Vc decreases as the cycle length increases.
Cycle length 100% increase
Vc 8% increase
(Review the sample problem on page 473)
Fig. 20.4
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17. A sample problem, p.473
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18. 20.4 The Concept of Left-Turn (and Right-Turn) Equivalency
In the same amount of time, the left lane discharges 5 through vehicles and 2 left-turning vehicles, while the right lane discharges 11 through vehicles.
Chapter 20

19. Left-turn vehicles are affected by opposing vehicles and number of opposing lanes.5
1000
1500
The LT equivalent increases as the opposing flow increases. For any given opposing flow, however, the equivalent decreases as the number of opposing lanes is increased.
Chapter 20

20. Left-turn consideration: 2 methods
Given conditions:
2-lane approach
Permitted LT
10% LT, TVE (ELT) =5
h = 2 sec for through
Solution 1: Each LT consumes 5 times more effective green time.
Solution 2: Calibrate a factor that would multiply the saturation flow rate for through vehicles to produce the actual saturation flow rate.
Chapter 20

21. 20.5 Delay as an MOE Common MOEs: Delay Queuing
Stopped time delay: The time a vehicle is stopped while waiting to pass through the intersection
Approach delay: Includes stopped time, time lost for acceleration and deceleration from/to a stop
Travel time delay: the difference between the driver’s desired total time to traverse the intersection and the actual time required to traverse it.
Time-in-queue delay: the total time from a vehicle joining an intersection queue to its discharge across the stop-line or curb-line.
Control delay: time-in-queue delay + acceleration/deceleration delay)
Common MOEs:
Delay
Queuing
No. of stops (or percent stops)
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22. 20.5.2 Basic theoretical models of delay
Uniform arrival rate assumed, v
Here we assume queued vehicles are completely released during the green.
Note that W(i) is approach delay in this model.
At saturation flow rate, s
The area of the triangle is the aggregate delay.
Figure 20.10
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23. Three delay scenarios This is acceptable. This is great.
UD = uniform delay
OD = overflow delay due to prolonged demand > supply (Overall v/c > 1.0)
OD = overflow delay due to randomness (“random delay”). Overall v/c < 1.0
A(t) = arrival function
D(t) = discharge function
If this is the case, we have to do something about this signal.
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24. Arrival patterns compared
Isolated intersections
Signalized arterials
HCM uses the Arrival Type factor to adjust the delay computed as an isolated intersection to reflect the platoon effect on delay.
Chapter 20

25. Webster’s uniform delay model, p480
UDa
Total approach delay
The area of the triangle is the aggregated delay, “Uniform Delay (UD)”.
To get average approach delay/vehicle, divide this by vC
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26. Modeling for random delay, p.481
UD = uniform delay
Analytical model for random delay
Adjustment term for overestimation (between 5% and 15%)
OD = overflow delay due to randomness (in reality “random delay”). Overall v/c < 1.0
D = 0.90[UD + RD]
Chapter 20

27. Random delay derivation
Chapter 20.
Chapter 20

28. Modeling overflow delay
because c = s (g/C), divide both sides by v and you get (g/C)(v/c) = (v/s). And v/c = 1.0.
The aggregate overflow delay is:
Because the total vehicle discharged during T is cT,
See the right column of p.482 for the characteristics of this model.
Chapter 20

29. Average overflow delay between T1 and T2
Average delay/vehicle = (Area of trapezoid)/(No. vehicles within T2-T1).
Derive it by yourself.
Hint: the denominator is c(T2-T1).
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30. 20.5.3 Inconsistencies in random and overflow delay
The stochastic model’s overflow delay is asymptotic to v/c = 1.0 and the overflow model’s delay is 0 at v/c =1.0. The real overflow delay is somewhere between these two models.
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31. Comparison of various overflow delay model
Delay model in the HCM 2000
The 4th edition dropped the HCM 2000 model (I don’t know why…). It looks like Akcelik’s model that you see in p. 484 (eq ).
These models try to address delays for 0.85<v/c<1.15 cases.
Chapter 20

32. 20.5.5 Sample delay computations
We will walk through sample problems (pages ). This will review all delay models we studied in this chapter.
Start reading Synchro 9.0 User Manual and SimTraffic 9.0 User Manual. We will use these software programs starting Mon, October 20, 2014.
Chapter 20