Lec 15, Ch.8, pp.291-304: Signal Timing (Objective)

Be able to state the objectives of signal timing Learn by heart signal-timing related terms (very

important) Understand how the yellow interval is determined Know how to design signal timing for a fixed

(pretimed) signal at an isolated intersection using the Webster’s model

What we cover in class today…

Terms relating to signal timing Objectives of signal timing Concept behind the determination of yellow

interval & dilemma zone Determining cycle length for a pretimed, isolated

signal using the Webster method Allocating green time to each signal phase

Terms relating to signal timingCycle length

Phase

Interval

Change interval

All-red interval (clearance interval)

Controller

Phase B

Terms relating to signal timing (cont)

Offset

Split phase

Phase 1A

Phase 1B

All signal analyses are based on through passenger cars. This way the analyses became portable to any sites. Then you need conversion of other-than-passenger cars and other-than-through vehicles. Hence we need:

Passenger car equivalent (PCE)

Turning movement factors

Terms relating to signal timing (cont)

Peak-hour factor (PHF): A measure of the variability of demand during the peak hour. The smallest time period used for traffic analyses is 15 min.

3 75

3 80 4 1

2

3 90

PHF =Volume during peak hour

4 x Vol. During peak 15 min within peak hour

=375 + 380 + 412 + 390

4 x 412= 0.945

If PHF is known, Design hourly volume (DHV) is computed by

DHV = (peak-hour volume)/PHF

Terms relating to signal timing (cont)Lane Group: consisting of one or more lanes on an intersection approach and having the same green phase

Critical Lane Group: the lane group that requires the longest green time in a phase. The critical lane group determines the green time that is allocated to that phase.

Saturation flow rate: the flow rate in veh/hr that the lane group can carry if it has the green indication continuously (see eq. 8.3 for the formula used by the Highway Capacity Manual 2000.)

Terms relating to signal timing (cont)

Critical movement: The maximum volume (vph) in a phase.

Once you have adjusted for truck and turn movement factors, you are ready to design phasing. One hint: if the adjusted left turn passenger car equivalent volumes is greater than 120 vph, we usually need a left-turn phase, which means that we need a left-turn bay. Up to that value, the yellow interval can provide enough time for LTs. There are a few methods to deal with left-turns. In this class you need to know only the methods shown below (i.e. protected left-turn phases) and in Example 8-5. All others will be discussed in CE562. It is a complex issue.

A B C D

130

140

600/2=300

576/2=288

Objectives of signal timing

Reduce the average delay of all vehicles Reduce the probability of accidents

Minimize the possible conflict points by assigning the right of way to different traffic movements

Two conflicting objectives:

More phases, less conflict

More phases, more lost time

So, if at all possible, use:

2 phases

Short cycle length

Yellow interval & Dilemma zone

LWuX c min0

a

uuX

2

20

00

Xc: the distance within which a vehicle traveling at the speed limit (u0) during the yellow interval cannot stop before encroaching on the intersection.

X0: the min. distance from the intersection for which a vehicle traveling at the speed limit u0 during the yellow interval cannot go through the intersection without accelerating

Distance traveled during yellow interval

Where τmin: yellow interval

Yellow interval & Dilemma zone (cont)

For the dilemma zones to be eliminated, X0 = Xc:

a

uuLWu

2

20

0min0

Solve for the yellow interval:

0

0min 2 u

LW

a

u

If the effect of grade is added:

0

0min 2 u

LW

Gga

u

Comfortable deceleration rate:

a = 0.27g

G = grade in decimals

Cycle lengths of pretimed signals by the Webster Method

Optimal cycle length C0 by the Webster method:

1

0

1

55.1

iiY

LC

L = Total lost time per cycle (sec), usually you lose 3 seconds per distinct phases.

Yi = Max value of the ratios of approach flows (called “critical movement”) to saturation flows for all lane groups using phase i, qij/Sj

= Number of phases

Vij = Flow on lane groups having the right of way during phase i

Sj = Saturation flow on lane group j; for a through lane, about 1900 pcphgpl

Cycle lengths of pretimed signals by the Webster Method (cont)

Lost time for phase i:

eiiaii GGl

Total lost time:

1ii RlL

R = Total all-red during the cycle

Green time allocation

Available total effective green time, Gte = C - L

Distribute effective green to each phase i by:

tei

ei GYYY

YG

...21

And the actual green time for each phase i is:

iieiai lGG Usually li is about 3 seconds.

Minimum green time

E

ped

pp W

N

S

LG 7.22.3

At an intersection where a significant number of pedestrians cross, it is necessary to provide a minimum green time that will allow the pedestrians to safely cross the intersection. After allocating green time, you must check with the minimum green time for each phase.

pedp

p NS

LG 27.02.3

For WE > 10 ft

For WE ≤ 10 ft

At an intersection where only a few pedestrians cross, this will be the length of green time for pedestrian actuated green.