12th TRB Conference on Transportation Planning Applications

May 17-21, 2009

Presenters: Jin Ren and Aziz Rahman

Automatically Balancing Intersection Volumes in A Highway Network

12th TRB Conference on Transportation Planning Applications

May 17-21, 2009

Presenters: Jin Ren and Aziz Rahman

12th TRB Conference on Transportation Planning Applications

May 17-21, 2009

Presenters: Jin Ren and Aziz Rahman

12th TRB Conference on Transportation Planning Applications

May 17-21, 2009

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

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 intra-zonal traffic causes turning volume losses

T-Flow Fuzzy Example 1

T-Flow Fuzzy Example 2

Why Introduce New Methods?

Develop a statistically sound techniqueReduce labor time on balancingGenerate more accurate turning

volumesCreate an automatic process which is

user-friendly and affordableBuild 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

ijjiij tbaT

tij

bj

aiAlgorithm assumption:

j

ji

i DO targettarget

Formula:

Schematics to Intersection Balancing

ijT

ijt1

int

ji

b

a

ijT

j

i

bnew

aold

j

i

bold

anew

%Err < 0.001ijtFinal NoYes

Equations for Intersection Balancing

Doubly constrained: ijjiij tbaT mth Iteration: Row wise

mth Iteration: Column wise

iestimate

miim

i O

aOa

,

1,target *

1 mj

mj bb

jestimate

mjjettm

j D

bDb

,

1,arg *

mi

mi aa

i i

iiestimate

i O

OOError

,target

,target,%

j j

jjestimate

j D

DDError

,target

,target,%

Successive Averaging or Maximizing and Iterative Balancing Diagram

Non Balanced Vol.

Avg. Link level In & Out Vol.

Form Intersection Turns Matrix

Balance Intersection In & Out Vol.

Apply Doubly Constrained for Turns Vol. Adjustment

Calculate %Error

% Error Change?

New Turn Vol.

%Error<0.001? Balanced Vol

Yes No

Yes

No

Layout Unbalanced Intersection Volumes

Assumption: Averaging in/out link volumes are supposed to be equal.

Int 4 Int 5

Average 0 0 Average 236 256Current in out Current in out

Average 0 0 Average Average 236 256 Average1333 out 1336 804 in 805 805 out 806 828 in 8291192 in 1189 882 out 881 881 in 879 1044 out 1043

360 586 212 375out in out in

Average 360 587 Average 211 375

Current OUT= 2579 IN= 2579 Current OUT= 2318 IN= 2318Desired OUT= 2574 In= 2583 Desired OUT= 2316 In= 2321

Int 14 Int 15

Average 360 587 Average 211 375Current in out Current in out

Average 359 588 Average Average 211 376 Average101 out 101 271 in 271 178 out 178 219 in 219136 in 136 174 out 174 273 in 273 150 out 150

142 239 18 19out in out in

Average 142 239 Average 18 19

Current OUT= 1005 IN= 1005 Current OUT= 722 IN= 722Desired OUT= 1004 In= 1006 Desired OUT= 722 In= 722

Doubly Constrained Balancing

Method: doubly constrained intersection arrivals and departures

Int 4 Int 5

Current Arrival (in) and Departure (out) Current Arrival (in) and Departure (out)

To: Current Desired To: Current DesiredFrom: west north east southEnteringEntering GF From: west north east southEnteringEntering GFwest 0 0 844.65 344.54 1189.2 1191.8 1.00 west 0 69.937 723.17 86.097 879.21 880.73 1.00north 0 0 0 0 0 0 0.00 north 101.05 0 116.42 18.877 236.35 236.35 1.00east 787.75 0 0 15.803 803.56 804.95 1.00 east 558.76 162.4 0 106.64 827.8 828.82 1.00south 548.19 0 37.59 0 585.78 586.66 1.00 south 146.53 23.737 204.8 0 375.07 375.4 1.00

Current exiting 1335.9 0 882.24 360.35 2578.5 2583.4 IN Current exiting 806.35 256.07 1044.4 211.61 2318.4 2321.3 INDesired exiting 1333 0 880.73 359.82 2573.5 2578.5 0.9981 Desired exiting 804.95 256.07 1043.1 211.43 2315.6 2318.4 0.9988

GF 1 1 1 1 OUT 1.0019 GF 1 1 1 1 OUT 1.0012

Int 14 Int 15

Current Arrival (in) and Departure (out) Current Arrival (in) and Departure (out)

To: Current Desired To: Current DesiredFrom: west north east southEnteringEntering GF From: west north east southEnteringEntering GFwest 0 115.41 12.377 8.1164 135.9 135.9 1.00 west 0 212.98 52.106 7.7647 272.85 272.85 1.00north 80.182 0 153.04 126.06 359.28 359.82 1.00 north 118.59 0 90.166 2.4842 211.24 211.43 1.00east 12.448 250.37 0 8.0035 270.83 270.83 1.00 east 51.958 159.52 0 7.8033 219.28 219.28 1.00south 8.6253 221.76 8.4569 0 238.84 238.98 1.00 south 7.8212 3.2219 7.8825 0 18.926 18.929 1.00

Current exiting 101.26 587.54 173.87 142.18 1004.9 1005.5 IN Current exiting 178.37 375.73 150.16 18.052 722.31 722.49 INDesired exiting 101.26 586.66 173.87 142.1 1003.9 1004.7 0.9992 Desired exiting 178.37 375.4 150.16 18.049 721.98 722.23 0.9996

GF 1 1 1 1 OUT 1.0008 GF 1 1 1 1 OUT 1.0004

Example 1 Balancing Statistics

T-Flow Fuzzy Technique Successive Average Technique

Example 2 Balancing Statistics

T-Flow Fuzzy Technique Successive Average Technique

Statistical Comparisons

Findings: SA/IB Example 1 and Example 2 are both better than T-Flow.

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

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