2010 Fall Transportation Conference A Guideline for Choosing Cycle Length to Maximize Two-Way Progression in Downtown Area Saeedeh Farivar Zong Tian University

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


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.



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)



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



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?


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


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:

mljUjs

jmjmjlj

jmjmjmUj

ljUji

iio

GIII

CTSTI

CTGTGI

III

IGGB

,

mod)(

]mod)[(

)]max[min()]max[min(

)(

min,

min,min,min,max


Max Bandwidth-Min Interference

Upper Interference Lower Interference

Gm

CC

Gm

GjGj

I uj I lj

m mj j


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


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


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



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


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



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



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


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


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


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


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

Documents

2010 Fall Transportation Conference A Guideline for Choosing Cycle Length to Maximize Two-Way Progression in Downtown Area Saeedeh Farivar Zong Tian University