and Over-saturated Signalized Approaches

Transcription

Estimating Delay, Stops, Fuel
Consumption, and Emissions at Oversaturated Signalized Intersections
Hesham Rakha and Montasir Abbas
Virginia Tech
Presentation Outline
• Vehicle delay estimation
• Vehicle stop estimation
• Vehicle fuel consumption and emission
estimation:
– Micro level (VT-Micro)
• Requires speed measurements each time interval
– Meso level (VT-Meso)
• Average speed, vehicle stops, and stopped delay
Slide 2
Rakha and Abbas
Delay Estimation
Microscopic Approach
• Delay computed microscopically at each time
step:
– Difference in travel time between instantaneous speed
and the facility free-flow speed
• Approach incorporated within the INTEGRATION
software
• Validated against shockwave and queuing theory
delay estimates
Where:
d(ti)
u(ti)
uf
∆t
Slide 3
= Delay at instant ti (s)
= Speed at instant ti (km/h)
= Free-speed (km/h)
= Time-step increment (s)
Rakha and Abbas

u (t i ) 


d (t i ) = ∆t  1 −
uf 

Delay Estimation
Model Validation
• INTEGRATION estimates of delay consistent with CCG
and HCM procedures
240
Australian Capacity Manual (1981)
Average Approach Delay (s/veh)
Highway Capacity Manual (1994)
200
Canadian Capacity Guide (1995) / Highway Capacity Manual (1997)
INTEGRATION - Average Results
INTEGRATION - Individual Simulation Results
160
120
80
40
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Volume to Capacity Ratio (v/c)
Slide 4
Rakha and Abbas
1.0
1.1
1.2
1.3
1.4
Delay Estimation
Model Validation
180
Webster (1958)
Average Approach Delay (s/veh)
160
Deterministic Queuing / Shock Wave
140
Deterministic Oversaturation / Shock Wave
120
Highway Capacity Manual (1994)
Australian Capacity Guide (1981)
CCG (1995) / HCM (1997)
100
INTEGRATION
80
60
40
20
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Volume to Capacity Ratio (v/c)
Slide 5
Rakha and Abbas
1.0
1.1
1.2
1.3
1.4
Stop Estimation
Background
• Historical models:
– Webster (1958): stops for uniform arrivals at singlelane, under-saturated isolated intersections
– Webster-Cobbe (1966): stops at under-saturated
intersections assuming random arrivals
– Newell (1965): stops for steady-state, under-saturated
conditions
– Catling (1977): stop at under-saturated and oversatured intersections based on classical queuing theory
– Cronje (1986): stops at under-saturated and oversaturated intersections by treating traffic as a Markov
process
Slide 6
Rakha and Abbas
Stop Estimation
Research Problem
• Limitation of existing models:
– Majority of models do not account for the partial
stops that vehicles may incur on intersection
approaches
– Models accounting for partial stops do not
consider over-saturated conditions
– Validity of models for over-saturated conditions
have not been demonstrated
Slide 7
Rakha and Abbas
Stop Estimation
Proposed Microscopic Model
• Over-saturated conditions:
Speed (km/h)
70
60
50
40
30
20
10
0
800
850
900
950
Time (seconds)
70
60
50
40
30
20
10
0
1050 1100 1150 1200 1250 1300 1350
Time (seconds)
Slide 8
1000
Speed (km/h)
Speed (km/h)
Speed (km/h)
– Multiple stops may be experienced
70
60
50
40
30
20
10
0
850
900
950
1000
Time (seconds)
1050
70
60
50
40
30
20
10
0
1400 1500 1600 1700 1800 1900 2000 2100
Time (seconds)
Rakha and Abbas
Stop Estimation
• Proposed partial stop estimation model
60
Speed (km/h)
50
40
Partial stop start point
ui-1
ui
30
20
10
Partial
stop
Si =
u i −1 − u i
uf
for
u i < u i −1
Partial stop end point
0
934 937 940 943 946 949 952 955 958 961 964
Time (seconds)
Slide 9
Rakha and Abbas
Stop Estimation
Speed (km/h)
• Example
Slide 10
65
60
55
50
45
40
35
30
25
20
15
10
5
0
1150
Total stops: 2.241
0.897 stop
0.307
0.090
1200
0.125
1250
0.170
0.227
1300
1350
Time (seconds)
Rakha and Abbas
0.425
1400
1450
Stop Estimation
Proposed Analytical Model
Queue Size (Vehicles)
• Upper bound for number of stops
Maximum queue
reach at end of
first cycle
Maximum queue
reach at end of
second cycle
Oversaturated
area
Residual queue
at end of each
cycle
Time
Slide 11
Rakha and Abbas
Stop Estimation
• Upper bound model
n
q ×te +
N ub =
Nub
q
S
C
r
te
n
Slide 12
å
i ×(qC - sg )
i= 2
q ×te
= Upper bound for average number of stops (stops/cycle)
= Average arrival flow rate (veh/sec)
= Saturation flow rate (veh/sec)
= Cycle time (sec)
= Effective green interval (sec)
= Evaluation period
= Number of cycle lengths in analysis period (te/C)
Rakha and Abbas
Stop Estimation
• Stop adjustment factor
1.1
Ratio of Simulated Number of
Stops to Theoretical Upper Bound
Stop Adjustment Factor
1.0
0.9
Regression Line for Adjustment
Factor
0.8
0.7
AF = 2.352-1.731x +0.405x 2
(R2=0.997)
0.6
0.5
0.4
0.3
Stop Estimation Model:
N s = N ub x AF
0.2
0.1
0.0
1.0
Slide 13
1.1
1.2
1.3
1.4
1.5
1.6
v/c Ratio
Rakha and Abbas
1.7
1.8
1.9
2.0
Stop Estimation
Model Validation
6.0
Queuing Theory Model
Cronje Model
Microscopic Model
Theoretical Upper Bound
Number of Stops
5.0
4.0
3.0
2.0
1.0
0.0
1.0
1.1
1.2
1.3
1.4
1.5
1.6
v/c Ratio
Slide 14
Rakha and Abbas
1.7
1.8
1.9
2.0
Fuel and Emission Estimation
VT-Micro Model Overview
• VT-Micro Model:
• Includes 32 parameters that are calibrated to
different vehicles [Ahn et al. (2000) and Rakha et al.
(2000)]
• Exponential transformation ensures positive MOE
estimates
• Developed using dynamometer and in-field
OEM data
Where:
L = Regression constant (a≥0)
M = Regression constant (a<0)
u = Instantaneous speed
a = Instantaneous acceleration
Slide 15
 i ∑= 0 j∑= 0(Lei , j ×u i ×a j )
e
MOE e =  3 3 e i j
e i ∑= 0 j∑= 0(M i , j ×u ×a )

3
Rakha and Abbas
3
for a ≥ 0
for a < 0
Model Development
• Chassis dynamometer data (97 vehicles):
– Model year ranged from 1986 to 1996
– All vehicles were tested at FTP under ambient
conditions using the standard vehicle certification test
fuel
– Vehicle emission tests were performed in random order
• Offset any possible order bias that could result in different
ambient conditions
– HC, CO, NOx, and CO2 emissions were measured:
• Composite "bags" and in grams on a second-by-second basis
– 60 vehicles classified as normal
• 43 LDVs and 17 LDTs
• 1.0 to 5.8 liter engines with mileage < 160,000 km
Slide 16
Rakha and Abbas
Sample Model
0.012
0.010
Field - Acceleration -3 km/h/s
Predicted - Acceleration -3 km/h/s
Field - Acceleration 0 km/h/s
Predicted - Acceleration 0 km/h/s
Fuel (l/s)
0.008
0.006
0.004
0.002
0.000
0
20
40
60
80
Speed (km/h)
Slide 17
Rakha and Abbas
100
120
140
Model Validation
• CO2 model predictions found to be consistent with
field measurements
Estimated
12
CO2 (g/s)
10
8
6
4
2
0
0
60
120
180
240
300
360
Time (s)
Slide 18
Rakha and Abbas
420
480
540
600
660
720
VT-Meso Model
Input
Average
AverageSpeed
Speed
Number
of
Stops
per
Number of Stops perKilometer
Kilometer
Average
Stop
Duration
Average Stop Duration
Synthetic Drive Cycle Construction
Mesoscopic
Model
Drive Mode Fuel
and Emission
Models
Amount of
Travel by Mode
Fuel and Emissions by
Mode
Output
Slide 19
Fuel
Fueland
andEmissions
Emissionsper
perVehicle-Kilometer
Vehicle-Kilometer
Rakha and Abbas
Microscopic
MicroscopicFuel
Fueland
and
Emissions
Model
Emissions Model
Questions?
Slide 20
Rakha and Abbas

and Over-saturated Signalized Approaches

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