1. Signal Warrants

2. Slide 2 Signal Warrants  http://mutcd.fhwa.dot.gov/htm/2009r1 r2/part4/part4c.htm http://mutcd.fhwa.dot.gov/htm/2009r1 r2/part4/part4c.htm

3. More Terms…

4. Slide 4 Basic Terminology (2/2)  Lost time (l i ) Time lost due to starting and stopping  Total lost time (L)  Saturation flow Flow at continuous movement assuming always green  All-red interval (AR) Time when all signals display red

5. Slide 5 More Terminology  Display Green (G i ) Time phase diplays green indication  Effective green (g i ) Time allocated to moving vehicles at saturation flow  Total effective green (g T )  Green ratio (g/C)

6. Slide 6 Timing Relationships τ

7. Slide 7 Relationships g i = G i - l i + τ i τ i = Y i + AR i g T = C - L

8. Slide 8 Flow Terminology  Discharge headway Time headway for vehicles departing  Saturation flow (1,900 pcphgpl under ideal conditions)

9. Slide 9 Greenshields’ Model

10. Change/Clearance Interval

11. Slide 11 Change/Clearance Interval  Minimum time between the green indications of two phases  Yellow + All-red  Provide driver with enough time to safely clear the intersection  Must be at least 3 seconds

12. Slide 12 Dilemma Zone ? For no DZ Distance to stop = Distance to clear

13. Slide 13 Dilemma Zone - Time to Clear ? XoXo WL Time to clear = (X o + W + L) / U o = τ min

14. Slide 14 Dilemma Zone - Time to Stop ? Distance to stop = X c = U o t r + U o 2 / (2a+64.4G) XcXc

15. Slide 15 Dilemma Zone Elimination  Set Xc = Xo to eliminate dilemma zone  Rearrange and solve for τ min

16. Slide 16 Change/Clearance Interval τ min = t r + [ u 0 /(2a+64.4G)] + [(W+L)/u 0 ] W is road width to be cleared (ft or m) L is vehicle length (ft or m) u 0 is approach speed of vehicles (fps or m/s) t r is driver’s reaction time (sec) (1.0 sec) a is deceleration rate (fps 2 or m/s 2 ) (10.0 ft/s 2 ) G is percent grade divided by 100

17. Slide 17 Change/Clearance Interval τ min = t r + [ u 0 /(2a+64.4G)] + [(W+L)/u 0 ] Yellow Time All Red

18. Slide 18 Phase Plan  Protected or Permitted Left Turns?  Cross Product Left and Opposing Throughs 1 Lane; > 50,000 2 Lanes; >90,000 3 Lanes; >110,000