12 th TRB Conference on Transportation Planning Applications May 17-21, 2009 Presenters: Jin Ren and Aziz Rahman Automatically Balancing Intersection Volumes in A Highway Network 12 th TRB Conference on Transportation Planning Applications May 17-21, 2009 Presenters: Jin Ren and Aziz Rahman 12 th TRB Conference on Transportation Planning Applications May 17-21, 2009 Presenters: Jin Ren and Aziz Rahman 12 th 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 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 ai and bj adjustments made to each O-D pair volume in order to achieve the target values Oi and Dj required by the growth factors for the origins and destinations t ij bjbj aiai Algorithm assumption: Formula:

Schematics to Intersection Balancing ai and bj adjustments made to each O-D pair volume in order to achieve the target values Oi and Dj required by the growth factors for the origins and destinations % Err < NoYes

Equations for Intersection Balancing Doubly constrained: ai and bj adjustments made to each O-D pair volume in order to achieve the target values Oi and Dj required by the growth factors for the origins and destinations m th Iteration: Row wise m th Iteration: Column wise

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.

Doubly Constrained Balancing Method: doubly constrained intersection arrivals and departures

Example 1 Balancing Statistics T-Flow Fuzzy TechniqueSuccessive Average Technique

Example 2 Balancing Statistics T-Flow Fuzzy TechniqueSuccessive Average Technique

Statistical Comparisons Findings: SA/IB Example 1 and Example 2 are both better than T-Flow. TESTSR2R2 RMSESlopeMean Rel Err% VOLUME DELTA T-Flow Fuzzy Ex (-3.0%) SA/IB Ex T-Flow Fuzzy Ex (-2.5%) SA/IB Ex

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