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2010 Fall Transportation Conference
A Guideline for Choosing Cycle Length to Maximize Two-Way Progression in
Downtown Area
Saeedeh Farivar
Zong Tian
University of Nevada, Reno
June 2012
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Outline
Background and Problem Statement Research Objective Analysis Method Results Summary and Conclusion
2
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Background and Problem Statement
Cycle length is one of the important signal timing parameters in determining the optimal solution of coordinated traffic signal control.
Cycle is constrained by a number of factors such as traffic volume, intersection spacing, travel speed, and pedestrian crossing time.
In general in downtown areas traffic volume is not a governing factor and travel time and pedestrian crossing time play more important roles.
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Background and Problem Statement
Henry’s Study: for uniformly-spaced intersections and when traffic demand is balanced in both direction, 2, 4, or 6 times of travel time btw intersections would provide a good progression bandwidth in both direction
Oregon DOT study: a relationship btw cycle length, signal spacing and speed to maximize progression efficiency (2 times of travel time)
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Background and Problem Statement
The Relationship Between Cycle Length and Max Bandwidth
Time
Spa
ce
Tij Tji
i
j
Cycle Length
Optimum Cycle Length= Tij+ Tji
Tij= Tji=TT Optimum Cycle Length=2 *TT
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Background and Problem Statement
The intersection spacing in downtown areas is generally short (e.g. 200 to 400 ft)
A min green time is required to serve pedestrians, therefore there is a min cycle length
Two times of travel time is a small value so that is NOT feasible to be considered as the
Cycle Length
What would be the best cycle length to operate signal system when travel time is small?
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Research Objectives
a) Developing a guideline for choosing the best cycle length that provides the best two-way progression in downtown areas with respect to various signal spacing: Uniformly and Randomly
b) Analyzing the impact of intersection spacing and number of signals on progression bandwidth
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Analysis Method
Messer’s Algorithm- a volume independent model that starts with signals with LT phases.
A specific case of Messer’s method with only 2-phase:
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CTSTI
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,
mod)(
]mod)[(
)]max[min()]max[min(
)(
min,
min,min,min,max
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Max Bandwidth-Min Interference
Upper Interference Lower Interference
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CC
Gm
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I uj I lj
m mj j
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Study Assumptions
Multiple scenarios were generated assuming: Number of signals: 2-20 Travel time btw signals: 7 to 50 sec Minor street phase split (necessary to serve pedestrians):
With considering 2 lanes in each direction, 5 sec walking time, and 3.5 ft/sec walking speed:
pedS
WFDW
FDWWalkG
sec207.185.3
4*125
ftG
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Study Assumptions
Major Street phase split : C-20 Cycle length (C): 45 to 120 sec with an increment of 5sec Bandwidth attainability (A) as for MOE:
The same green time for all intersections (min A=0.5 means one way progression bandwidth)
min,min,
max
io GGBA
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
10 15 20 25 30 35 40 45 50 550
20
40
60
80
100
120
f(x) = 2.0018175392538 x
Optimum Cycle Length, Average (Number of Signals 3 to 10)
Linear (Optimum Cycle Length, Average (Number of Signals 3 to 10))
Travel Time (sec)
Opt
imum
Cyc
le L
engt
h (s
ec)
Results- Optimum Cycle Length
Uniformly-spaced intersections
TTC *2
2
MinCTT
22
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Results- Optimum Cycle Length
Uniformly-spaced intersections- Small travel times
6 8 10 12 14 16 18 20 220
10
20
30
40
50
60
70
80
Average Optimum Cycle Length (Number of Signals 3 to 10)
Travel Time (sec)
Opt
imum
Cyc
le L
engt
h (s
ec)
TT
MinCC
*4 24
4MinC
TTMinC
MinCTT
11 22
y = 3.939 x
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Results- Bandwidth Attainability
Number of Signals
Travel Time (sec) 2 3 4 5 6 7 8 9 10
7 0.93 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
8 0.92 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
9 0.91 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
10 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
11 0.54 0.54 0.52 0.52 0.50 0.50 0.50 0.50 0.50
12 0.58 0.57 0.53 0.53 0.50 0.50 0.50 0.50 0.50
13 0.62 0.59 0.57 0.54 0.53 0.50 0.50 0.50 0.50
14 0.66 0.60 0.60 0.59 0.59 0.57 0.57 0.56 0.56
15 0.70 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63
16 0.74 0.63 0.62 0.62 0.61 0.61 0.60 0.60 0.59
17 0.78 0.64 0.62 0.62 0.60 0.60 0.58 0.58 0.56
18 0.82 0.64 0.64 0.62 0.62 0.60 0.60 0.58 0.58
19 0.86 0.72 0.65 0.65 0.65 0.64 0.64 0.63 0.63
20 0.90 0.80 0.67 0.67 0.67 0.67 0.67 0.67 0.67
21 0.94 0.88 0.82 0.76 0.70 0.65 0.65 0.65 0.64
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Results- Optimum Cycle Length
Randomly-spaced intersections
10 15 20 25 30 35 40 45 50 550
20
40
60
80
100
120
f(x) = 2.17381060567812 x
Optimum Cycle Length, Average (Number of Signals 3 to 10)
Linear (Optimum Cycle Length, Average (Number of Signals 3 to 10))
Travel Time (sec)
Opt
imum
Cyc
le L
engt
h (s
ec)
TTC *2
2
MinCTT
22
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Results- Optimum Cycle Length
6 8 10 12 14 16 18 20 220
10
20
30
40
50
60
70
80
Average Optimum Cycle Length (3 to 10 Signals)
Average Travel Tiem (sec)
Opt
imum
Cyc
le L
engt
h (s
ec) y = 4.271 x
Randomly-spaced intersections- Small travel times
TTC *4
2
MinCTT
22
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Results- Bandwidth Attainability
Number of Signals
Travel Time (sec) 2 3 4 5 6 7 8 9 10
7 0.93 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
8 0.92 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
9 0.91 0.54 0.50 0.50 0.50 0.56 0.50 0.50 0.50
10 0.50 0.66 0.50 0.50 0.58 0.57 0.54 0.55 0.50
11 0.54 0.74 0.50 0.60 0.50 0.54 0.50 0.50 0.50
12 0.58 0.67 0.60 0.62 0.62 0.50 0.50 0.60 0.50
13 0.62 0.53 0.50 0.64 0.54 0.53 0.57 0.56 0.55
14 0.66 0.80 0.59 0.52 0.50 0.60 0.50 0.51 0.53
15 0.70 0.80 0.68 0.65 0.50 0.64 0.55 0.50 0.56
16 0.74 0.66 0.76 0.64 0.62 0.57 0.53 0.56 0.55
17 0.78 0.70 0.52 0.56 0.63 0.53 0.59 0.60 0.50
18 0.82 0.72 0.73 0.60 0.58 0.61 0.58 0.61 0.56
19 0.86 0.72 0.68 0.62 0.63 0.57 0.53 0.54 0.56
20 0.90 0.80 0.70 0.65 0.63 0.60 0.63 0.63 0.62
21 0.94 0.86 0.82 0.76 0.70 0.69 0.57 0.62 0.55
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
The impact of intersection spacing and number of signals on bandwidth attainability
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
Uniformly-spaced, Average Attainability (Travel Time from 7 to 50 seconds)
Randomly-spaced, Average Attainability (Travel Time from 7 to 50 seconds)
Number of Signals
Ban
dwid
th A
ttai
nabi
lity
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Summary and Conclusions
Uniformly-spaced intersections
Randomly-spaced intersections
2*2
24*4
4
MinCTTTT
MinCTT
MinCTT
MinCTTJudgementgEngineerin
Coptimum
2*2
2*4
MinCTTTT
MinCTTTT
Coptimum
C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012
Summary and Conclusions
Uniformly-spaced intersections provides more effective bandwidth progression especially when travel time btw intersections increase.
Uniformly-spaced intersections provides more effective bandwidth progression especially with large number of signals (more than 7 signals).
Less bandwidth attainability with more number of signals
When the average travel time btw intersection is less than 15 sec, increase of cycle length does not improve bandwidth attainability significantly.
C.A.T.E.RCenter for Advanced Transportation Education and Research
Thank You