AbstractAbstractHigh-resolution vehicle speed profiles obtained from sophisticated devices such as global positioning system (GPS) receivers provide an opportunity to accurately measure intersection delay, composed of deceleration delay, stopped delay, and acceleration delay. Although the delay components can be measured by manually examining the speed profiles or derived time-space diagrams, identifying when vehicles begin to decelerate or stop accelerating is not always a straightforward task. In addition, a manual identification process may be laborious and time-consuming when handling a large network or numerous runs. More importantly, the results from a manual process may not be consistent between analysts or even for a single analyst over time. This paper proposes a new approach to identifying control delay components based on second-by-second vehicle speed profiles obtained from GPS devices. The proposed approach utilizes both de-noised speed and acceleration profiles for capturing critical points associated with each delay component. Speed profiles are used for the identification of stopped time periods, and acceleration profiles are used for detecting deceleration onset points and acceleration ending points. The authors applied this methodology to sampled runs collected from GPS-equipped instrumented vehicles and concluded that it satisfactorily computed delay components under normal traffic conditions. IntroductionIntroduction• Measurement of control delay is important for

evaluating the performance of signalized intersections.

• Control delay, in particular the delay components including deceleration delay, stopped delay, and acceleration delay, are not always easy to measure in the field.

•Global positioning system (GPS) technology provides an opportunity to track vehicle movements even on a second-by-second basis.

•The utilization of GPS speed data enables researchers to measure the control delay components efficiently and effectively.

•In this research, a new approach to measuring control delay components is suggested and applied to real-world GPS data.

Control Delay ComponentsControl Delay Components

Acceleration delay

Time

Dis

tanc

e

Stopped delay

t1 t2 t3 t4

Deceleration delay

vff

vff

At t1 , Deceleration begins

At t2 , Stop begins

At t3 , Stop ends and acceleration begins

At t4, Acceleration ends

Deceleration time

Stopped time

Acceleration time

Control delay

Vff = desired speed

d1

d2

d3

Typical Vehicle Speed and Typical Vehicle Speed and Acceleration Profiles near Acceleration Profiles near IntersectionsIntersections

•Examination of both acceleration and speed profiles near intersections reveals critical points associated with delay components.

Time

Spe

ed

Acc

eler

atio

n

0

Speed Profile

Acceleration Profile

t1 t2 t3 t4

T2 - T1 = Deceleration period

T3 – T2 = Stopped period

T4 - T3 = Acceleration period

Time

Spe

ed

Acc

eler

atio

n

0

Speed Profile

Acceleration Profile

t1 t2 t3

T2 - T1 = Deceleration period

T3 – T2 = Acceleration period

Speed Profile with Stopped Delay

Speed Profile without Stopped Delay

Approach to Identifying Critical Approach to Identifying Critical PointsPoints

1. Smoothing speed profile

2. Generating acceleration profile

3. Identifying critical points related to stopped delay using speed profiles

4. Identifying critical points related to acceleration and deceleration delay using

acceleration profiles

5. Compute delay by each component

Selected Smoothing Method

Local polynomial regression technique: quadratic polynomial and 2-second bandwidth for gaussian kernelApplication & ResultsApplication & Results• Data: Real-world GPS data obtained from

Commute Atlanta Project (Sampled 14 trips)

0 50 100 150 200 2500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (second)

Dis

tanc

e (m

ile)

Sampled 14 Vehicle Trip Trajectories for the Test Site

0 20 40 60 80 100 1200

20

40

60

time (second)

spee

d (m

ph)

Trip #2 - Stopped delay: 0sec, Decel delay: 9.5sec, Accel delay: 5.7sec

0 20 40 60 80 100 1200

0.5

1

time (second)

dist

ance

(mile

)

0 20 40 60 80 100 120-5

0

5

time (second)

acce

lera

tion

(mph

/s)

0 20 40 60 80 100 120 1400

10

20

30

40

time (second)

spee

d (m

ph)

Trip #5 - Stopped delay: 12sec, Decel delay: 5.8sec, Accel delay: 8.5sec

0 20 40 60 80 100 120 1400

0.5

1

time (second)

dist

ance

(mile

)

0 20 40 60 80 100 120 140-10

-5

0

5

time (second)

acce

lera

tion

(mph

/s)

Critical points

• The suggested approach appropriately detects the critical points.

• Thus, the approach efficiently computes delay components.

Effects of Bandwidth SizeEffects of Bandwidth Size• Speed profile smoothing is a critical element

for the suggested approach as the degree of smoothing directly affects the results of computed delays.

• Thus, the size of bandwidth, which determines the degree of smoothing, should be appropriately selected.

•The sensitivity analysis was performed, indicating that a 2-second bandwidth may be adequate.

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10

Bandwidth (sec)

Acce

lera

tion

dela

y (s

ec)

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6 7 8 9 10Bandwidth (sec)

Dece

lera

tion

dela

y (s

ec)

05

101520253035404550

0 1 2 3 4 5 6 7 8 9 10Bandwidth (sec)

Stop

ped

dela

y (s

ec)

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6 7 8 9 10Bandwidth (sec)

Con

trol

del

ay (s

ec)

Limitation to the Suggested Limitation to the Suggested MethodologyMethodology

• The suggested method may not truly detect the locations of critical points under congestion conditions or for closely-spaced intersections.

Sensitivity of Delay Computation Results to the Size of Bandwidth

ConclusionsConclusions• The suggested methodology, applied to GPS

second-by-second speed profiles, efficiently detects critical points of each delay components.

• However, fine-tuning is required for the method to be applicable to congested conditions and closely-spaced intersections.

Falsely detect the onset point of delay