Transcript Slide 1

Automatically Balancing Intersection
Volumes in A Highway Network
12th
12th thTRB Conference on Transportation Planning Applications
TRB
12 Conference
TRB Conference
on Transportation
on Transportation
Planning
Planning
Applications
Applications
12th TRB Conference May
on Transportation
17-21, 2009 Planning Applications
May 17-21,
May 17-21,
2009 2009
May
2009Rahman
Presenters: Jin Ren17-21,
and Aziz
Presenters:
Presenters:
Jin Ren
Jinand
Ren Aziz
andRahman
Aziz Rahman
Presenters: Jin Ren and Aziz Rahman
Presentation Outline
Need for Balanced Volumes
Current Balancing Techniques
New Automatic Balancing Techniques
Formation of Intersection Turn Matrix
Doubly Constrained Method
Successive Averaging or Maximizing
and Iterative Balancing
 Statistical Comparisons of Methods
 Conclusion
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Need for Balanced Volumes
 Existing base highway network
simulation in Synchro and VISSIM
 Unbalanced upstream and downstream
post-processed future flow
 Build simulation confidence in audience
 Ensure simulation model run results not
wacky
 Take into account mid-block driveway
traffic in simulation
Current Balancing Techniques
1. Manual Adjustment: match the
volumes departing one intersection to
those arriving at the downstream
intersection, or vice versa
2. EMME Demand Adjustments: create a
trip table and run traffic assignment
based on intersection volumes
3. VISUM T-Flow Fuzzy Technique: create
a trip table to emulate intersection
turning volumes
Pros and Cons of Each Technique
1. Manual Adjustment:
a) uses a simple spreadsheet or Synchro
b) time-consuming if numerous
balancing iterations required
2. VISUM T-Flow Fuzzy Technique: emulate
turns with balanced volumes, but intrazonal traffic causes turning volume losses
T-Flow Fuzzy Example 1
T-Flow Fuzzy Example 2
Why Introduce New Methods?
Develop a statistically sound technique
Reduce labor time on balancing
Generate more accurate turning
volumes
Create an automatic process which is
user-friendly and affordable
Build confidence in simulation with the
balanced volumes
New Automatic Balancing Techniques
 Successive Averaging/Iterative
Balancing: iteratively average
downstream and upstream link volumes
and then balance intersections
 Successive Maximizing/Iterative
Balancing: iteratively maximize
downstream and upstream link volumes
and then balance intersections
Formation of Intersection Turn Matrix
Doubly Constrained Balancing Method
-Factors for origins (in) and destinations (out)
-Bi-Proportional Algorithm
Formula:
Tij  aib j tij
Algorithm assumption:
target
target
O

D
 i
 j
i
j
tij
bj
ai
Schematics to Intersection Balancing
t ij
int ai
bj  1
Tij
old ai
new b j
Tij
new ai
old b j
Final tij
Yes
%Err < 0.001
No
Equations for Intersection Balancing
Doubly constrained:
Tij  aib j tij
mth Iteration: Row wise
ai 
m
O target,i * a im 1
bj  bj
m
Oestimate,i
m 1
Oestimate,i  Otarget,i
% Errori  
Otarget,i
i
mth Iteration: Column wise
ai  ai
Dt arg et , j * b mj 1
m
bj 
Destimate, j
m
m
% Errorj  
j
Destimate, j  Dtarget, j
Dtarget, j
Successive Averaging or Maximizing
and Iterative Balancing Diagram
Non Balanced Vol.
Avg. Link level In & Out Vol.
Form Intersection Turns Matrix
New Turn Vol.
Balance Intersection In & Out Vol.
Apply Doubly Constrained for Turns Vol. Adjustment
Calculate %Error
Yes
%Error<0.001?
Balanced Vol
No
Yes
% Error Change?
No
Layout Unbalanced Intersection Volumes
Int 4
Int 5
Average
Current
Average
1333 out
1192
in
0
out
0
1336
1189
Average
Current
Desired
0
in
0
Average
Current
804
882
in
out
Average
805
881
360 586
out
in
360 587
OUT= 2579
IN= 2579
OUT=
2574 In= 2583
Current
Desired
828 in
1044 out
Average
829
1043
212 375
out
in
211 375
OUT= 2318
IN= 2318
OUT=
2316 In=
2321
Int 15
Average
Current
360 587
in
out
359 588
101
136
Average
Current
Desired
806
879
Average
Int 14
Average
101 out
136
in
Average
805 out
881
in
236 256
in
out
236 256
Average
Current
271
174
in
out
Average
271
174
Average
178 out
273
in
142 239
out
in
142 239
OUT= 1005
IN= 1005
OUT=
1004 In= 1006
178
273
Average
Current
Desired
211 375
in
out
211 376
219
150
in
out
Average
219
150
18
19
out
in
18 19
OUT= 722
IN= 722
OUT=
722 In=
722
Assumption: Averaging in/out link volumes are supposed to be equal.
Doubly Constrained Balancing
Int 4
Int 5
Current Arrival (in) and Departure (out)
Current Arrival (in) and Departure (out)
To:
From:
west
west
0
north
0
east 787.75
south 548.19
Current exiting 1335.9
Desired exiting 1333
GF
1
Current Desired
north
east southEnteringEntering GF
From:
0 844.65 344.54 1189.2 1191.8
1.00
west
0
0
0
0
0
0.00
north
0
0 15.803 803.56 804.95
1.00
east
0 37.59
0 585.78 586.66
1.00
south
0 882.24 360.35 2578.5 2583.4 IN
Current exiting
0 880.73 359.82 2573.5 2578.5 0.9981 Desired exiting
1
1
1
OUT 1.0019
GF
To:
west
0
101.05
558.76
146.53
806.35
804.95
1
north
69.937
0
162.4
23.737
256.07
256.07
1
east
723.17
116.42
0
204.8
1044.4
1043.1
1
Int 14
Int 15
Current Arrival (in) and Departure (out)
Current Arrival (in) and Departure (out)
From:
west
north
east
south
Current exiting
Desired exiting
GF
To:
west
0
80.182
12.448
8.6253
101.26
101.26
1
north
115.41
0
250.37
221.76
587.54
586.66
1
east
12.377
153.04
0
8.4569
173.87
173.87
1
Current Desired
southEnteringEntering GF
From:
8.1164 135.9 135.9
1.00
west
126.06 359.28 359.82
1.00
north
8.0035 270.83 270.83
1.00
east
0 238.84 238.98
1.00
south
142.18 1004.9 1005.5 IN
Current exiting
142.1 1003.9 1004.7 0.9992 Desired exiting
1
OUT 1.0008
GF
To:
west
0
118.59
51.958
7.8212
178.37
178.37
1
north
212.98
0
159.52
3.2219
375.73
375.4
1
east
52.106
90.166
0
7.8825
150.16
150.16
1
Current Desired
southEnteringEntering GF
86.097 879.21 880.73
1.00
18.877 236.35 236.35
1.00
106.64 827.8 828.82
1.00
0 375.07 375.4
1.00
211.61 2318.4 2321.3 IN
211.43 2315.6 2318.4 0.9988
1
OUT 1.0012
Current Desired
southEnteringEntering GF
7.7647 272.85 272.85
1.00
2.4842 211.24 211.43
1.00
7.8033 219.28 219.28
1.00
0 18.926 18.929
1.00
18.052 722.31 722.49 IN
18.049 721.98 722.23 0.9996
1
OUT 1.0004
Method: doubly constrained intersection arrivals and departures
Example 1 Balancing Statistics
T-Flow Fuzzy Technique
Successive Average Technique
Example 2 Balancing Statistics
T-Flow Fuzzy Technique
Successive Average Technique
Statistical Comparisons
TESTS
R2
RMSE
Slope
Mean Rel
Err%
VOLUME
DELTA
T-Flow
Fuzzy Ex 1
0.96
20
0.95
12
-1358
(-3.0%)
SA/IB Ex 1
0.97
17
0.96
10
4
T-Flow
Fuzzy Ex 2
0.97
21
1.00
12
-1114
(-2.5%)
SA/IB Ex 2
0.99
12
0.98
7
0
Findings: SA/IB Example 1 and Example 2 are both better than T-Flow.
Conclusion
• An innovative mathematical method is
presented with two practical examples
• Successive averaging/iterative balancing
technique shows better goodness of fit
statistics
• Automatic balancing technique saves
time in traffic simulation process
• The spreadsheet method can be
implemented cost-effectively
• Capacity constraint can be incorporated
in the balancing algorithm in future