Transcript Basic principles of intersection signalization

Chapter 20: Basic principles of intersection
signalization
Chapter objectives: By the end of this chapter the
student will be able to:
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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
1
Four critical aspects of signalized intersection
operation discussed in this chapter
1.
2.
3.
4.
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
Chapter 20
2
20.1.1 Components of a Signal Cycle
Cycle length
Phase
Controller
Interval
Change interval
All-red interval
(clearance interval)
Chapter 20
3
Signal timing with a pedestrian signal: Example
Interval
Pine St.
Veh.
1
G-26
2
3
Y-3.5
4
R-25.5
5
Oak St.
Ped.
W-20
Veh.
R-31
%
Ped.
DW-31
36.4
FDW-6
10.9
DW-29
6.4
AR 2.7
G-19
6
7
Y-3
8
R-2
Cycle length = 55 seconds
Chapter 20
W-8
14.5
FDW-11
20.0
DW-5
5.5
AR 3.6
4
20.1.2 Signal operation modes and left-turn
treatments & 20.1.3 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
5
Factors affecting the permitted LT
movement
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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
6
CFI (Continuous
Flow Intersection)
Bangerter Highway &
3500 South
Chapter 20
7
DDI (Diverging Diamond Interchange)
Chapter 20
8
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
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20.2 Discharge headways, saturation flow,
lost times, and capacity
Δ(i) Start-up lost time
Effective
green
h
12 3 4 56 7
s
3600
h
l1 

 (i )
T  l1  nh
Vehicles in queue
Y i  y i  ar i
Total lost time t  l  l
L
1
2
Saturation flow rate
Startup lost time
Gi
g i  G i  Yi  t L
Clearance lost time l  y  ar  e
2
e
Capacity
yi ari
Chapter 20
g i Extension
ci  si
of green
C
Cycle length
10
Sample problem, p. 467
First approach:
Second approach:
Eq. 20-6
Chapter 20
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20.2.6 Saturation flow rates from
a nationwide survey
Chapter 20
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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
L H  Nt L
3600
C
T G  3600  Nt L
100
Total loss in one hour
3600
C
Total effective
green in one hour
1
3600 
Vc 
  3600  Nt L
h
h
C 
TG
75
450
Max. sum of critical traffic demand; this is the total
demand that the intersection can handle.
N = No. of phases; tL = Lost time in seconds per phase; C = Cycle length, sec;
h = saturation headway, sec/veh
Chapter 20
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20.3.2 Finding an Appropriate Cycle Length
Desirable cycle length, incorporating
PHF and the desired level of v/c
C min 
Nt L
Vc


1 

3600
/
h


Nt L
C des 
Eq. 20-13
Eq. 20-14
Vc
1
PHF ( v / c )( 3600 / h )
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.
Doesn’t this look like the Webster model?
C0 
1 .5 L  5

1
Y
i
i 1
Y i  flow _ ratio ( v / s ) i
Chapter 20
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Webster’s optimal cycle length model
C0 
1 .5 L  5
C0 = optimal cycle length for minimum delay, sec

1
 v s 
i 1
L = Total lost time per cycle, sec
i
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
15
20.3.2 Finding an Appropriate Cycle Length
Desirable cycle length, Cdes
Cycle
length
100%
increase
Vc 8% increase
Marginal gain in
Vc decreases as
the cycle length
increases.
(Review the sample
problem on page 473)
Fig. 20.4
Chapter 20
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A sample problem, p.473
Vc 
TG

h
1
3600 
3600

Nt
L
h 
C 
Nt L
C des 
1
Vc
PHF ( v / c )( 3600 / h )
Chapter 20
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20.4 The Concept of Left-Turn (and RightTurn) 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
5  2 E LT  11
and :
E LT 
11  5
 3 .0
2
18
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
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Left-turn consideration: 2 methods
Given conditions:
Solution 1: Each LT
consumes 5 times more
effective green time.
 2-lane approach
 Permitted LT
 10% LT, TVE (ELT) =5
 h = 2 sec for through
h prev  ( 0 . 1)( 5  2 . 00 )  ( 0 . 9 )( 2 . 00 )  2 . 80 sec/ h
s
3600
h prev

3600
 1286 vphgpl
2 . 80
Solution 2: Calibrate a factor that would multiply the saturation flow
rate for through vehicles to produce the actual saturation flow rate.
s  3600
f LT 

h ideal
h prev
2

s  1800 ( 0 . 714 )  1286 vphgpl
 1800 vphgpl
or
h ideal
 PLT E LT hideal   (1  PLT )(1 . 0 ) hideal 
1
1  PLT ( E LT  1)

1
1  0 . 10 ( 5  1)
s  1800 ( 2 . 0 / 2 . 8 )  1800 ( 0 . 714 )  1286
 0 . 714
Chapter 20
20
20.5 Delay as an MOE
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.
Common MOEs:
• Delay
• Queuing
• No. of stops (or
percent stops)
Time-in-queue delay: the total time
from a vehicle joining an intersection
queue to its discharge across the stopline or curb-line.
Control delay: time-in-queue delay +
acceleration/deceleration delay)
Chapter 20
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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
Chapter 20
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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
If this is the case, we have
to do something about this
signal.
Chapter 20
A(t) = arrival
function
D(t) = discharge
function
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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
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Webster’s uniform delay model, p480
g

R  C 1  
C

V  v  R  t c   vR  vt c  st c
UDa
tc 
vR
sv

g

C 1  
sv 
C
v
g   vs 

V  st c  C 1   
C   s  v 

2
g   vs 
2
UD a  ( base : R )( height : V )  C 1   
2
2
C   s  v 

1
1
Total approach delay
The area of the triangle is the aggregated
delay, “Uniform Delay (UD)”.
2
UD 
To get average approach
delay/vehicle, divide this by vC
C 1   g C 
2
Chapter 20
1  v s 
25
Modeling for random delay, p.481
C 1   g C 
2
D 
2

1  v s 

 0 . 65 c v
 v c 
2 1 3
UD = uniform
delay
Adjustment term for
overestimation
(between 5% and 15%)
OD = overflow delay due to
randomness (in reality “random
delay”). Overall v/c < 1.0

v c 2
2 v 1  v / c 
2g C


Analytical model
for random delay
D = 0.90[UD + RD]
Chapter 20
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Random delay
derivation
Chapter 20.
Chapter 20
27
Modeling overflow delay
C 1   g C 
2
UD o 

1  v s 
C 1  ( g C ) 

2
1   g / C 2
1   g / C v / c 
C
2
2
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:
OD a 
1
2
T vT  cT  
T
2
2
v  c 
Because the total vehicle
discharged during T is cT,
OD 
T
2
v c   1  
T
2
X
 1
See the right column of p.482 for the
of this model.
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Chaptercharacteristics
20
Average overflow delay between
T1 and T2
  
OD 
T1  T 2
v c 1
2
Average delay/vehicle =
(Area of trapezoid)/(No.
vehicles within T2-T1).
Derive it by yourself.
Hint: the denominator is
c(T2-T1).
Chapter 20
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20.5.3 Inconsistencies in random and
overflow delay
C 1   g C 
2
D 
2

1  v s 

 0 . 65 c v

v c 2
2 v 1  v / c 
 v c 
2 1 3
2g C

OD 
T
2
v c   1 

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.
Chapter 20
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Comparison of various overflow delay model
20.5.4 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. 20-26).
These models try to address delays for 0.85<v/c<1.15 cases.
Chapter 20
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20.5.5 Sample delay computations
We will walk through sample problems
(pages 484-485). 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
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