Signal Warrants

Slide 2

Signal Warrants

http://mutcd.fhwa.dot.gov/htm/2009r1r2/part4/part4c.htm

More Terms…

Slide 4

Basic Terminology (2/2)

Lost time (li) 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

Slide 5

More Terminology

Display Green (Gi) Time phase diplays green indication

Effective green (gi) Time allocated to moving vehicles at

saturation flow Total effective green (gT) Green ratio (g/C)

Slide 6

Timing Relationships

Los tt ime

Los tt ime

RedG reen

E ff ect ive green

τ

Slide 7

Relationships

gi = Gi - li + τi

τi = Yi + ARi

gT = C - L

Slide 8

Flow Terminology

Discharge headway Time headway for vehicles

departing Saturation flow (1,900 pcphgpl

under ideal conditions)

Slide 9

Greenshields’ Model

0

1

2

3

4

Hea

dw

ay (

sec)

1 2 3 4 5 6 7 8

Vehicle Number

Change/Clearance Interval

Slide 11

Change/Clearance Interval

Minimum time between the green indications of two phases

Yellow + All-redProvide driver with enough

time to safely clear the intersection

Must be at least 3 seconds

Slide 12

Dilemma Zone

Clear

Stop

?

For no DZ Distance to stop = Distance to clear

Slide 13

Dilemma Zone - Time to Clear

Stop

?

Xo W L

Time to clear = (Xo + W + L) / Uo = τmin

Slide 14

Dilemma Zone - Time to Stop

Clear

?

Distance to stop = Xc = Uotr + Uo2 / (2a+64.4G)

Xc

Slide 15

Dilemma Zone Elimination

Set Xc = Xo to eliminate dilemma zone

Rearrange and solve for τmin

Slide 16

Change/Clearance Interval

τmin = tr + [u0 /(2a+64.4G)] + [(W+L)/u0]

W is road width to be cleared (ft or m)L is vehicle length (ft or m)u0 is approach speed of vehicles (fps or m/s)

tr is driver’s reaction time (sec) (1.0 sec)a is deceleration rate (fps2 or m/s2) (10.0 ft/s2)G is percent grade divided by 100

Slide 17

Change/Clearance Interval

τmin = tr + [u0 /(2a+64.4G)] + [(W+L)/u0]

Yellow Time All Red