when signal coordination should break according to traffic demand: a case study sparks blvd

C.A.T.E.RCenter for Advanced Transportation Education and Research ITE Santa Barbara 2012

When Signal Coordination Should Break According to Traffic Demand: A Case Study

Sparks Blvd

Rasool Andalibian

Zong Tian, PhD, P.E.,

University of Nevada, Reno

June 2012


Outline

Background and Problem Statement

Signal Coordination: Common Practice

Stop Probabilistic Model (non-coordinated arterials)

Simulation Evaluation Summary and Conclusions


Problem Statement

Major signalized arterials are generally coordinated

during peak periods.

They run free (actuated) during non-peak periods.

Traffic demand level is a key element to consider.

At what demand level signal coordination is warranted?


Signal Coordination Strategy

Signal Timing Manual: Establishing coordination is justifiable

when the intersections are in close proximity of each other and

there is a large amount of traffic on coordinated street.

MUTCD: Traffic signal within 0.5 mile of each other along a

corridor should be coordinated.

FHWA: When intersections are close together (i.e., within ¾ mile

of each other) it is advantageous to coordinate them. At greater

distances (over ¾ mile), the traffic volumes and potential for

platoons should be reviewed for coordination operation.


Research Objectives

Develop a probabilistic model that predicts the number of

stops for non-coordinated signalized arterials.

Develop # stop thresholds using the model that can

guide engineers to decide when signals should be

coordinated or not.

Determining whens signal progression should break for

Sparks Blvd pertaining to traffic demand.


Model Assumptions

Probability of stop at an intersection is independent from

the other intersections.

Probability of stop is a function of the red time to cycle

length ratio, r/c.

Vehicle arrivals are random.

Traffic is under-saturated.


Probabilistic Model: Basic Equations

i

)a(g i )a(r i

1)()(

)()()(

)(/)()(

)(/)()(

aPaP

aragaC

aCaraP

aCagaP

i

r

i

g

ii

ii

r

ii

g

i = direction of travela = intersection index


Probability of hitting green in direction i at each intersection is the same:

The probability of making x number of stops out of n intersections follows a Binomial distribution:

The expected number of stops:

Homogenous Probability Model

ig

ig

ig

ig P)n(P)....(P)(P 21

xnig

xig

ix )P()P(

x

nSPF

1

)1(.0

i

g

i

x

n

x

i PnSPFxEX


Probability of hitting green at each intersection is NOT the same:

The probability of making x number of stops out of n intersections:

The expected number of stops:

Non-homogenous Probability Model

i

g

i

g

i

g

i

g PnPPP )()....2()1(

n

a

i

g

i

x

n

x

i aPnSPFxEX10

)(.

n

j

n

jj

n

jj

i

rx

i

r

i

r

n

jjj

i

gx

i

x

xx xx

jPjPjPjPSPF1 1 1

11,...,,11 21 11

)(...)(.)(.)((...


Non-homogenous case could be simplified to homogenous case using average g/c ratio:

Proof:

Simplified Non-homogenous

))((1

(*))(....)2()1(1

aPn

PnPPPn

a

i

g

i

g

i

g

i

g

i

g

(*))1()))(1

1()(.110

i

g

n

a

i

g

n

a

i

g

n

x

i

x

i PnaPn

naPnSPFxEX


Model Validation: A Case Study

Sparks Blvd, Sparks, Nevada.

4.5 mile length.

9 intersections.

Speed limit 40 mph.


Demand Scenarios

Various demand scenarios were generated using midday

traffic demand as the base.

Using HCM methodology to calculate v/c ratios.

Signals are set in free mode.


Demand Scenario Cont.

Demand Variation%(from midday)

+20 0.63 0.54 0.59

00 (midday) 0.53 0.46 0.51

-20 0.41 0.36 0.39

-40 0.29 0.25 0.27

-60 0.19 0.16 0.18

-70 0.14 0.11 0.13

-80 0.09 0.07 0.08

-90 0.04 0.04 0.04


Timing Plan

Fully Actuated Mode

• Min Recall on Sparks Blvd (Main Street)

• Signal Timing Parameters: Current Parameters that have been

Implemented in the field

Coordinated Plan, Based on Mid-Day Peak Hours


Proposed Model vs. VISSIM Simulation(Q-Q Plot)

Using g/c ratio from HCM Using g/c ratio from Synchro


Proposed Model vs. VISSIM Simulation



No. Stops Correlation Matrix

VISSIMProbability Model

(g/c)HCM

Probability Model

(g/c)Synchro

VISSIM - 0.96 0.97

Probability Model

(g/c)HCM

0.96 - 1.00

Probability Model

(g/c)Synchro

0.97 1.00 -


Signal Coordination Guideline

When number of stops is more than 50% in free mode, signals should be coordinated. In this case, two consecutive stops is guaranteed.

When number of stops is less than 20% in free mode, it means that the performance of the system is acceptable and no coordination.

When number of stops falls between 20% and 50%, engineering judgment should be applied to determine whether to run signals in coordination or not.

Tian Laptop

50% stops and two consecutive stops are not the same thing.If different % stop threshholds is used (e.g., 20%, 30%), what are your conclusions?


No. Stops: Coordinated vs. Free Mode

NB Direction SB Direction

0.510.100.510.09


Summary and Findings

Lack of consistency in traffic demand level to determine when

signalized arterials should be coordinated.

This study is to develop a probabilistic model that predicts

#stops for non-coordinated signalized arterials and develop a

guideline recommending when signals should be coordinated.

Number of stops is a function of g/c ratio which embeds v/c

ratio indirectly. The higher the g/c the lower the chance of

making stops.

Tian Laptop



Summary and Findings Cont.

The result of simulation model (comparing coordination and non-coordination plan) approves the recommended guideline for signal timing strategy.

Sparks Blvd:

• When v/c is greater than 0.5 signals should be coordinated.

• When v/c is less than 0.10 signals should be ran free.

• When v/c falls between 0.10 and 0.50 engineering judgment

should be apply for signal timing strategy.

Tian Laptop



THANK YOU

22

QUESTION


Numerical Example

A hypothetical arterial of five intersections with the following g/C ratios.

Intx # NB SB

1 0.80 0.65

2 0.80 0.65

3 0.80 0.65

4 0.80 0.65

5 0.80 065

AVE 0.80 0.65

Homogenous Case

Intx # NB SB

1 0.68 0.70

2 0.75 0.60

3 0.82 0.56

4 0.92 0.63

5 0.83 0.78

AVE 0.80 0.65

Non-Homogenous Case

Tian Laptop

Do you mean NB and SB in the tables as your figures next pager show NB and SB?


Comparison

Homogenous Non-Homogenous


Travel Time: Coordinated vs. Free Mode

NB Direction SB Direction


Travel Time: Aggregated Model

Travel time difference:

Tian Laptop



Side Street Delay: Aggregated Model

Tian Laptop



Signal Coordination Guideline

% Stops(Free Mode)

Coordination

≤20 ≥5020≤…≤50

YESNOEng.

Judgment

Tian Laptop



Travel Time vs. Side Street Delay


Signal Timing Strategy according to the Developed Guideline


Proposed Model vs. VISSIM Simulation



COORDINATION VS.

NON_COORDINATION

Simulation Results

32


Sparks Blvd: Coordination Plan

A coordinated plan for midday traffic condition.

The plan mainly favorites southbound direction.

The model ran 10 times for each scenario.

MOES: arterial travel time, side street delay & #stops.

Tian Laptop


when signal coordination should break according to traffic demand: a case study sparks blvd

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