Post on 03-Jun-2018
transcript
8/13/2019 Urban Arterial Travel Time Variability
1/23
Urban Arterial Road
Travel Time VariabilityModelling
Susilawati, PhD
Research Presentation, February 14th2014
8/13/2019 Urban Arterial Travel Time Variability
2/23
Outline
Travel time variability
Travel time distribution
Travel time variability modelling
Discussion
8/13/2019 Urban Arterial Travel Time Variability
3/23
Day to day variation onJourney to Work travel times
Day to day variation in JTW travel times
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
2
8/02/2007
2
8/03/2007
2
8/04/2007
2
8/05/2007
2
8/06/2007
2
8/07/2007
2
8/08/2007
2
8/09/2007
2
8/10/2007
2
8/11/2007
2
8/12/2007
2
8/01/2008
2
8/02/2008
Traveltime(min)
t
incident
incidentincident
8/13/2019 Urban Arterial Travel Time Variability
4/23
Travel time variability
8/13/2019 Urban Arterial Travel Time Variability
5/23
Use the 95th percentile t ) of the travel timedistribution as the travel time reliabilitymetrics
Utilise normal distribution properties; and as
the parameters to measure travel time reliability
Travel time variability
8/13/2019 Urban Arterial Travel Time Variability
6/23
Travel time distribution
Need for best fit travel time distribution Empirical travel time data are likely to have long tail and
positive skew
in some cases shows bimodality and multimodality
The Burr distributionProposed Travel time distribution
8/13/2019 Urban Arterial Travel Time Variability
7/23
The Travel time distribution
Normal, Log normal, Weibull, Gamma & Betadistribution
The modelling technique
Multiple regression technique
Linear and power function
The influence factors
Free flow travel time
Volume Capacity ratio Link length
Delay congestion index
Travel time variability modelling
8/13/2019 Urban Arterial Travel Time Variability
8/23
Travel time variability modelling cont.
Multiple linear regressions
the most commonly used technique
e.g. Herman and Lam in Detroit, Richardson and Taylor in Melbourne Australia andPolus in Michigan
Eliasson
Stockholm bypass road by utilising travel time data collected thorough anautomatic camera system
t=actual travel time
t0= free flow travel time
L =link length
TODand speedare dummy variables representing time of day and the speedlimit,
is a constant, and , and are estimated parameters
8/13/2019 Urban Arterial Travel Time Variability
9/23
Peer et al (2009)
15 minute interval travel time was derived from speed data collected by
loop detector
VCR = flow capacity ratio
L=link length
=estimated parameter
Black and Chin (2007) GPS data from individual vehicles at 34 routes in ten of the largest urban
areas in England
Travel time variability modelling cont.
8/13/2019 Urban Arterial Travel Time Variability
10/23
cdf
rthmoment will only exist if ck>r
Modal will only exist if c> 1.
[If c1, then the distribution is L-shaped.]
Percentile
)1(1
)1(),,(
kcc
xckxkcxf
kcxkcxF
)1(1),,(
)1(
)1()(
)(
k
cr
crkk
xE rr
c
m
ck
c
x
/1
1
1
c k
P Px 1)1( /1
Burr distribution
8/13/2019 Urban Arterial Travel Time Variability
11/23
8/13/2019 Urban Arterial Travel Time Variability
12/23
1090
5090
tt
ttskew
50
5090var
t
tt
c k
P Px 1)1( /1
c kx 12 /150 c k
x 110 /1
90
c k
c kc k
12
12110
/1
/1/1var
kcxP )1(1
c
k
x 1910
/1
10
Travel Time Variability Metric
8/13/2019 Urban Arterial Travel Time Variability
13/23
Study area Selected links from the Glen Osmond
Road (GOR link 1 and 6) and South
Road (SR link 18, 20 and 22) were
selected as study area.
Longitudinal journey to work travel
time using GPS-equipped probe
vehicles were analysed.
Glen Osmond Road:
link lengths vary from 152m to
1146m
posted speed limits of either 50km/h
or 60km/h
consist of 180 runs
South Road corridor
comprising 22 links Link lengths vary from 135m to
4007m
posted speed limits between
60km/h and 80km/h
consist of 100 runs
8/13/2019 Urban Arterial Travel Time Variability
14/23
Burr regression
The shape parameter (c)is allowed to vary with ywhere yiscovariate (dimensional vector)(Beirlant et al, 1998)
)1(1)1(),,( kcc xckxkcxf
k=shape parameter
c=shape parameter
x= travel time
y = Degree of saturation
8/13/2019 Urban Arterial Travel Time Variability
15/23
SCATS
SCATS system generates control parameters:
Maximum flow;
Headway at the maximum flow
Occupancy time at maximum flow
Degree of saturation
DSthe ratio of effectively used green time tothe total available green time
8/13/2019 Urban Arterial Travel Time Variability
16/23
8/13/2019 Urban Arterial Travel Time Variability
17/23
GOR 6
0 20 40 60 80 100
0.0
0
0.0
2
0.0
4
0.0
6
0.0
8
travel time
Empirical Travel Time
Burr regression DS=0.8Burr regression DS=0.9
Burr regression DS=1Burr regression DS=1.1
8/13/2019 Urban Arterial Travel Time Variability
18/23
SR 22
0 200 400 600 800
0.0
00
0.0
01
0.
002
0.0
03
0.0
04
density
Empirical Travel Time
Burr regression DS=0.8Burr regression DS=0.9
Burr regression DS=1
Burr regression DS=1.1
8/13/2019 Urban Arterial Travel Time Variability
19/23
Link No
Burr Parameter for Empirical Data Percentile
Var
c k scale 10th 50th 90th
1 GOR 8.9 0.5 100.9 85.1 113 165 0.7
6 GOR 63.7 0 28.4 21.3 26 44.4 0.9
Link NoBurr Parameter for Estimated Data Percentile Var
DS c k scale 10th 50th 90th
1 GOR 1.9 0.6 3.1 1 120.1 59.3 119.1 237.7 1.5
0.7 3.8 67.1 119.2 211.1 1.2
0.8 4.6 74.2 119.4 191.4 1
0.9 5.6 80.7 119.5 176.5 0.8
1 6.7 86.5 119.6 165.1 0.7
1.1 8.2 91.5 119.7 156.2 0.5
6 GOR 3.1 0.6 6.5 1 37.8 20.2 34.9 114.1 2.7
0.7 8.8 20.5 30.3 71.2 1.7
0.8 12 20.6 27.4 50.7 1.10.9 16.4 20.8 25.5 39.7 0.7
1 22.4 20.9 24.2 33.3 0.5
1.1 30.6 20.9 23.3 29.3 0.4
1.2 41.8 21 22.6 26.7 0.3
8/13/2019 Urban Arterial Travel Time Variability
20/23
Link NoBurr Parameter for Empirical Data Percentile
Var
c k scale 10th 50th 90th
18 SR 3 2 317.2 119.2 235.1 407.6 1.2
20 SR 3.4 4.8 200.6 64.6 115.3 173.7 0.9
22 SR 5.4 0.7 261.4 186.5 286.5 470.3 1
Link NoBurr Parameter for Estimated Data Percentile Var
DS c k scale 10th 50th 90th
18 SR 1.2 0.6 2.1 3.7 420.4 78.8 199.9 394.2 1.6
0.7 2.4 95.9 218.1 397.2 1.4
0.8 2.7 114 235.5 399.9 1.2
0.9 3.1 132.9 252.1 402.2 1.1
1 3.5 152.1 267.6 404.3 0.9
1.1 3.9 171.3 282.2 406.2 0.8
20 SR 1.3 0.6 2.2 5.4 213.8 34.7 85.2 159.5 1.5
0.7 2.5 43.2 95.1 165.2 1.3
0.8 2.8 52.4 104.9 170.4 1.1
0.9 3.2 62.1 114.3 175.1 1
1 3.6 72.1 123.3 179.4 0.91.1 4.1 82.2 131.7 183.2 0.8
22 SR 1.4 0.6 2.3 1.3 331.8 114.9 288 669 1.9
0.7 2.7 132 293.4 610.5 1.6
0.8 3.1 148.8 298.1 563.8 1.4
0.9 3.5 165.2 302.3 526.1 1.2
1 4 181 306 495.4 1
1.1 4.7 195.9 309.2 470.1 0.9
8/13/2019 Urban Arterial Travel Time Variability
21/23
Conclusion
The value of c, k and scale parameters are close to the value of the
empirical c, k and scale parameter and the pdf functions for empirical
and estimated data have similar shape
The estimated percentiles are similar to the empirical data percentiles.
The 10th, 50th and 90th percentiles resulting from 0.6 degree of
saturation are lower than 0.9 degree of saturation.
The 10th and 50th percentiles increase as the degree of saturation
increases while the 90thpercentile decreases .
Higher degree of saturation is likely to have less variability since the 10th
percentile is close
8/13/2019 Urban Arterial Travel Time Variability
22/23
Conclusion
Burr regression technique allowing us to explore the role of SCATS
degree of saturation in determining the value of the Burr parameter c,
and leading to different shapes of the distribution and different values of
the travel time variability metrics. Thus it is possible to estimate the travel
time variability at varying levels of the SCATS degree of saturation
8/13/2019 Urban Arterial Travel Time Variability
23/23
Further Research Burr regression technique for other traffic
parameters
Cost Benefit analysis in relation to travel timereliability modelling
Data collection method
Online data collection, incident management
GIS and GPS integration in relation to ESRI cloud
environment which called ArcGIS online fororganisation