1. 1 Fine Tuning Mathematical Models for Toll Applications Dr. A. Mekky, P.Eng., A. Tai, M. Khan Ministry of Transportation, Ontario, Canada

2. 2 Presentation Outline  Introduction  The GTA  Hwy 407  Transportation Tomorrow Survey  The GTA Model  The Problem  Model Fine-Tuning and Parameter Testing  Results and Conclusions.

3. 3 Introduction  Transportation models have many applications in transportation planning  One of those applications is the simulation of toll roads  In this kind of application one usually needs to estimate the expected revenue from a particular toll road investment  The main statistic coming out of the model in this case is the vehicle.km on the toll road  High accuracy of estimation is important.

4. The Greater Toronto Area  6 Regions  Population 5.4 Million  Employment 2.9 Million  Autos 2.8 Million  Daily Trips 12 Million

5. Hwy 401 Hwy 403 QEW Hwy 7 Hwy 407 Gardiner Exp. Hwy 400 Hwy 10 Hwy 6 Hwy 7A Hwy 7 Hwy 48 Hwy 404 DVP Hwy 403 Toronto York Durham Peel Halton Hamilton Hwy 407 Total Length = 108 km Average Peak Hr. Trip Length = 19.48 km Total Peak Hr. Users = 3,300 Total Peak Hr. Vehicle km = 641,500 Lake Ontario Highway 407  East-west north of Toronto  108 km in 4 Regions  Fully Electronic Tollway  Opened in November 1997  Toll about 13c per km  Daily Trips about 300,000.

6. 6 Transportation Tomorrow Survey  Travel Behaviour Telephone Survey  Covers GTA & surrounding areas  1986, 1991, 1996, 2001  Info Contents:  Household Information (locations, etc)  Person Information (age, gender, etc)  Trip Information (OD, time, modes, etc).

7. 7 The GTA Model  Since the 1960’s  Base Year: 2001  Zones: 1,677  Gateways: 26  Nodes: 12,457  Links: 37,385  Demand: Trip Matrix from TTS (2001)  All Trip Purposes, Automobile Trips Only  Commercial Vehicles not included explicitly.

8. 8 The Problem Original Model Performed Reasonably well at the Screen-Line Level However, it didn’t produce good results for observed volumes & the number of users on Hwy 407 This had an effect on adjacent facilities

9. 9 The Problem cont’d It was tempting to use tools to reproduce volumes on links (DEMADJ) The decision was made to check/ fine-tune main elements of the network first.

10. 10 Fine-Tuning (stage 1)  Since good part of the network was “inherited” from the previous “century”, an update exercise was needed:  Fine-tuning Free-Flow Speeds  Adjust free flow speed on access roads and parallel facilities to Hwy 407  Adjust free flow speed on Hwy 407  Adjust free flow speed on Hwy ramps  Adjust some centroid connectors

11. 11 Fine-Tuning (stage 1) cont’d  Adjust Hwy 407 Capacity to 2200 vehicles/ hr/ lane (instead of 1800), as it carries low heavy vehicle traffic  Form of Volume Delay Functions Unchanged  Travel Matrix Unchanged.

12. 12 Fine-Tuning (stage 2)  Build upon Fine-Tuning of stage 1  Adjust parameters of VDFs (alpha, beta)  Adjust Value of Time for tollway  Travel Matrix Unchanged.

13. 13 Parameters Testing  Alpha for Non-Highways  Alpha For Highways  Beta for Non-Highways  Beta for Highways  Value of Time A macro was written to do several emme/2 run with various combinations Of the above parameters.

14. 14 Hypotheses Tested  Base: Original network & original VDF  Stage 1 Update: Modified network with original VDF, no matrix modification  Stage 2 Update: Modified network with modified VDF, no matrix modification  DEMADJ on Stage 1 Update  DEMADJ on Stage 2 Update.

15. 15 Main Results Non Hwy Alpha Hwy Alpha Value of Time VKM on Hwy 407 Users On Hwy 407 Avg Trip Length, Km Actual641,50032,92019.48 BASE1122486,30043,29011.23 UPDATED S11122596,10040,72014.64 NEW-VDF S20.701.9529644,80041,64015.49 DJ-UPDATED S1 1122630,80046,79013.48 DJ-NEW-VDF S2 0.701.9529659,50045,31014.55

16. 16 Main Results cont’d % Changes Induced by DEMADJ On Stage1 (Actual vs Resultant)

17. 17 % Changes Induced by DEMADJ On Stage 2 (Actual vs Resultant) Main Results cont’d

18. 18 Screen Line Analysis (Estimated/ Counts Ratio)

19. Hwy 407 counts vs Base Assignment R-Square = 76%

20. Hwy 407 counts vs Stage 1 Update R-Square = 71%

21. Hwy 407 counts vs Stage 2 Update R-Square = 72%

22. R-Square = 94% Hwy 407 counts vs DJ on Stage 1 Update

23. Hwy 407 counts vs DJ on Stage 2 Update R-Square = 89%

24. 24 Conclusions Compared to fine-tuning using network and VDF parameters, adjustment of the matrix with DEMADJ distorted the original matrix and gave larger errors in average trip length, VKM and the number of Hwy 407 users Fine-tuned model performed well at the screen-line level as well as gave better average trip length, VKM and number of users on Hwy 407 It is advised that models should be validated using info re average trip length, VKM if possible Heavy usage of DEMADJ without checking other parameters is not recommended.

25. END