1. Transportation Engineering
Lecture 8: Traffic Signal

2. Critical Lane Critical Lane & Time Budget
This concept is used for the allocation of the 3600 seconds in the hour to lost time and to productive movement.
The amount of time required for each signal phase is determined by the most intensely used lane which is permitted to move during the phase.
All other lane movement in the phase require less time than the critical lane.
The timings of any signal phase is based on the flow and lost times of the critical lane.
Each signal phase has one and only one critical lane.

3. Capacity (using critical Lane volume)
Critical Lane & Time Budget
Capacity (using critical Lane volume)
Capacity can be maximum sum of critical lane volumes that a signal can accommodate.
the max. total volume that can be handled on all critical lanes for a given time budget (within an hour),
tL total lost time per phase
N is total number of phases in a cycle
C is cycle length

4. Capacity (using critical Lane volume)
Critical Lane & Time Budget
Capacity (using critical Lane volume)
the effect of number of phases and cycle time on Vc
Lost time remains constant through out (h= 2.15s, lost time = 3s/phase)

5. Example
The cycle length is 40 sec, 2 phase cycle and saturation headway 2.3sec. What should be the lane numbers for each approach?

6. Solution

7. Adding consideration of v/c ratio and PHF
Critical Lane & Time Budget
Adding consideration of v/c ratio and PHF
(volume-to-capacity) V/C ratio:
flow rate in a period expressed as an hourly equivalent over capacity (saturation flow rate)
the proportion of capacity being utilized
A measure of sufficiency of existing or proposed capacity
V/C ratio = 1.00 is not desirable

8. Adding consideration of v/c ratio and PHF
Critical Lane & Time Budget
Adding consideration of v/c ratio and PHF
Peak Hour Factor (PHF) :
To account for flow variation within an hour
PHF
For 15 min. aggregate volume, PHF =
The lower the value, the greater degree of variation in flow during an hour.

9. Adding consideration of v/c ratio and PHF
Critical Lane & Time Budget
Adding consideration of v/c ratio and PHF

10. Adding consideration of v/c ratio and PHF
Critical Lane & Time Budget
Adding consideration of v/c ratio and PHF
Min. cycle length,
Considering desired v/c ratio,
Considering peaking within hour,
Desirable cycle length,

11. Adding consideration of v/c ratio and PHF
Critical Lane & Time Budget
Adding consideration of v/c ratio and PHF

12. Effects of right-turning vehicles
Effect of Turning Vehicles
Effects of right-turning vehicles
Right turns can be made from a
Shared lane operation
Exclusive lane operation
Traffic signals may allow permitted or protected right turn
Right-turning vehicles look for a gap in the opposing traffic on a permitted turning movement, which is made through a conflicting pedestrian or an opposing vehicle flow.
Right-turning vehicles consume more effective green time than through vehicles.

13. Effects of right-turning vehicles
Effect of Turning Vehicles
Effects of right-turning vehicles

14. Effects of right-turning vehicles
Effect of Turning Vehicles
Effects of right-turning vehicles
Through Car Equivalent
Example: with an opposing flow of 700 vph which has no platoon structure, it is observed that the right lane of the figure processes two RT vehicles and three TH vehicles in the same time that the left lane processes 17 TH vehicles. What is the “THcar” equivalent of one right- turning vehicle (RT equivalent) in this case?
3 + 2 ERT = 17 or ERT = 7
In this situation, 1 RT vehicle is equivalent to 7 TH vehicles in terms of headway.

15. Effects of right-turning vehicles
Effect of Turning Vehicles
Effects of right-turning vehicles
Through Car Equivalent
depends on the opposing
flows, and the number of opposing lanes
The right turn adjustment factor is related to the fraction of RT vehicles and the TH equivalency

16. Effect of Turning Vehicles

17. Example Effect of Turning Vehicles
Example: consider an approach with 10% RT, two lanes, permitted RT phasing, a RT equivalency factor of 5, and an ideal saturation headway of 2 sec per veh. Determine
the equivalent saturation headway for this case,
the saturation flow rate for approach, and
the adjustment factor for the sat. flow rate? (adj. flow rate / sat flow rate of TH vehicles)

18. Performance measures Delay Delay Queuing Stops Delay most directly
affects driver
experience.

19. Performance measures Delay
Stopped Time Delay: time a vehicle stopped waiting to pass the intersection.
Approach Delay:
stopped time + acceleration + deceleration
Travel Time Delay: (actual travel time-desired travel time)
Time-in-queue Delay: Total time from joining a queue to passing the stop line

20. Delay
Delay

21. Delay
Webster’s Delay Model
Webster’s uniform delay (UD) formula

22. Webster’s Delay Model Delay Webster’s uniform delay (UD) formula
Red time,
Height of the triangle,
Area of the triangle, (UD)
Average delay per vehicle,

23. Webster’s optimum cycle length
Delay
Webster’s optimum cycle length
developed based on minimization of overall delay at intersection

24. Webster’s optimum cycle length
Delay
Webster’s optimum cycle length

25. Notes on cycle length Delay
Optimum cycle length is min. delay point of the suitable curve
Unnecessarily long cycle lengths cause substantial delays; short cycle lengths may cause congestion or violate the pedestrian crossing times.
Cycle lengths between 45 and 180 s are used in the field. All cycle lengths typically end in 0 or 5; thus, if the cycle length estimate is 52s, a cycle equal to 50 or 55s should be selected.

26. Notes on cycle length Delay
Optimum cycle length is min. delay point of the suitable curve
Unnecessarily long cycle lengths cause substantial delays; short cycle lengths may cause congestion or violate the pedestrian crossing times.
Cycle lengths between 45 and 180 s are used in the field. All cycle lengths typically end in 0 or 5; thus, if the cycle length estimate is 52s, a cycle equal to 50 or 55s should be selected.

27. Delay
Example
Consider an approach volume of 1000 vph, saturation flow rate of 800vphg, cycle length 90 s and g/C ratio 0.55.
What average approach delay per vehicle is expected?