Increasing Precision in Highway Volume through Adjustment of Stopping Criteria in Traffic Assignment and Number of Feedbacks Behruz Paschai, Kathy Yu, Arash Mirzaei North Central Texas Council of Governments (NCTCOG)

May 2009 TRB National Transportation Planning Applications Conference2 Assignment Improvement Goals 1.Reduce noise level 2.Define a multi-dimensional criteria for the relative gap and number of feedbacks 3.Perform the process with the exponential and conical VDFs

May 2009 TRB National Transportation Planning Applications Conference3 Software Platform 1.Roadway and Transit models in TransCAD 2.Multi-modal generalized-cost user equilibrium traffic assignment 3.Microsoft ® Windows ® XP operating system

May 2009 TRB National Transportation Planning Applications Conference4 Hardware Setup 1.Intel, single dual core, 3.6 GHz, 3 GB RAM 2.Intel Xeon, two dual cores, 3.00 GHz, 3GB RAM 3.Intel Xeon, two quad cores, 3.2 GHz, 3 GB RAM

May 2009 TRB National Transportation Planning Applications Conference5 Model Attributes Number of links : ~31,300 Number of nodes : ~20,400 Number of zones : 5,386 (83 Externals) Coverage area : ~10,000 sq. miles Counties completely covered : 13 Total daily trips : ~16.7x10 6

May 2009 TRB National Transportation Planning Applications Conference6 Zone Structure Number of zones : 5,303 (+83 Externals) Coverage area : ~10,000 sq. miles ~ 120 Miles ~ 90 Miles

May 2009 TRB National Transportation Planning Applications Conference7 Link Network Number of links : ~31,300 Number of nodes : ~20,400 Link Functional Classification F0  Centroid Connector F1  Freeway F2  Major Arterial F3  Minor Arterial F4  Collector F6  Ramp F7  Frontage Road F8  HOV Lane F9  Transit Line

May 2009 TRB National Transportation Planning Applications Conference8 Demographics Model Year Model Demographics HHPOPEMP TOTAL TRIPS ZONES Year 20052,216,1675,954,6773,472, x10 6 5,386 DEMOGRAPHICS

May 2009 TRB National Transportation Planning Applications Conference9 Assignment Improvements ItemCurrentRecommended Number of Iterations30Defined by the Gap Relative Gap Number of Feedbacks25 VDF FormExponentialConical

May 2009 TRB National Transportation Planning Applications Conference10 NCTCOG 4-Step Modeling LOOP Demographics Zone Layer Trip Generation Trip Distribution Mode Choice Roadway Assignment Roadway Skims Roadway Network Transit Network Transit Skims Transit Assignment Stopping Criteria Satisfied YES NO FEEDBACK LOOP

May 2009 TRB National Transportation Planning Applications Conference11 Feedback Loop – Skim Averaging LOOP Mode Choice Roadway Assignment Trip Distribution [A i ] Roadway Skims (i) [D i ] = F( [Di-1], [Ai]) [D i-1 ] = Average Roadway Skims (i-1) [A i ] = Roadway Skims (i) Compare [Di] vs [Di-1] Skim Averaging (MSA, Constant Weight) FEEDBACK LOOP Demographics Zone Layer Trip Generation Stopping Criteria Satisfied YES NO Transit Assignment

May 2009 TRB National Transportation Planning Applications Conference12 Assignment Tests 1.Relative gap : 0.001, and Number of iterations : defined by the relative gap 3.Number of feedbacks : 10 4.VDF : exponential, conical 5.Averaging methods: a.Method of Successive Averages (MSA) b.Constant weight (0,.15,.25,.35,.45,.55)

May 2009 TRB National Transportation Planning Applications Conference13 Exponential vs Conical VDFs Speed Limit = 60 mph Exponential delay function

May 2009 TRB National Transportation Planning Applications Conference14 MSA = Averaged matrix for assignment = New matrix from trip distribution Feedback numberk = Less weight for new solutions in every feedback loop =

May 2009 TRB National Transportation Planning Applications Conference15 Constant Weight Averaged matrix for assignment e ij (k) = = New matrix from trip distribution Feedback numberk = = w = Averaging weight (w=0  naïve) Constant weight for new solutions in every feedback loop

May 2009 TRB National Transportation Planning Applications Conference16 Conclusion 1 – Exponential VDF 1.Relative gap : Feedback loops : 5 (run time ~ 20 hrs) 3.Constant weight : 0.25/ Model run time reduction : mostly contributed to the core-distributed traffic assignment step

May 2009 TRB National Transportation Planning Applications Conference17 Comparison of Trip and Skim Matrices – Conical VDF Total Difference Sum of the absolute value of the cell-by-cell differences in two consecutive feedback loops Root Square Error The root square error of the cell-by-cell differences in two consecutive feedback loops

May 2009 TRB National Transportation Planning Applications Conference18 Skim Differences – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference19 Trip Differences – Conical VDF Note : PADIST is the sum of the HBW, HNW, and NHB person trips

May 2009 TRB National Transportation Planning Applications Conference20 Skim Error – Conical VDF Note : PADIST is the sum of the HBW, HNW, and NHB person trips

May 2009 TRB National Transportation Planning Applications Conference21 Trip Error – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference22 Total Difference Sum of the absolute value of the differences in two consecutive feedback loops for each functional classification and the whole network Root Mean Square Error The root mean square error (RMSE) of the differences in two consecutive feedback loops per functional classification and the whole network Comparison of Volumes – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference23 Volume Differences – Conical VDF Note : ALL graph excludes the centroid connectors (FUNCL = 0)

May 2009 TRB National Transportation Planning Applications Conference24 Volume RMSEs – Conical VDF Note : ALL graph excludes the centroid connectors (FUNCL = 0)

May 2009 TRB National Transportation Planning Applications Conference25 Volume Change – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference26 Max Volume Differences – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference27 Min Volume Differences – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference28 Run Times – Conical VDF

May 2009 TRB National Transportation Planning Applications Conference29 Conclusion 2 – Conical VDF 1.Relative gap : Feedback loops : 5 (run time ~ 15 hrs) 3.Constant weight : 0.25/ Total link RMSE : < 1.2% 5.Solution accuracy : ½ one lane capacity for each functional classification

May 2009 TRB National Transportation Planning Applications Conference30 Acknowledgment NCTCOG Model Development Group staff for development of macros, and presentation review: Kathy Yu Arash Mirzaei

May 2009 TRB National Transportation Planning Applications Conference31 Contact Info Behruz Paschai Kathy Yu Arash Mirzaei North Central Texas Council of Governments (NCTCOG)