1. Estimating Link Travel Time with Explicitly Considering Vehicle Delay at Intersections Aichong Sun Email: asun@pagnet.orgasun@pagnet.org Tel: (520) 792-1093

2. Content Outline  Current Status of VDF in Travel Demand Model  VDF Estimation  VDF Validation  VDF Implementation  Conclusions

3. Current Status of VDF in Travel Demand Model Link-Based VDFs  The Bureau of Public Roads (BPR) Function  Conical Volume-Delay Function Free-Flow-Travel-Time and Capacity are typically determined by link-class/area-type lookup table without considering the intersecting streets Could change Stay same Get built or upgraded

4. Current Status of VDF in Travel Demand Model VDF Considering Intersection Delay  Logit-based Volume Delay Function Israel Institute of Transportation Planning & Research  HCM Intersection Delay Function  Other functions (good discussion on TMIP 3/6/08- 3/17/08) Common Issues  over-sophisticated with the intension of thoroughly characterizing traffic dynamics Computational Burden & Data Requirement  Function are not convex in nature No convergence for traffic assignment procedure

5. Current Status of VDF in Travel Demand Model PAG’s Travel Demand Model  Use only BPR functions until very recently  BPR functions are not calibrated with local data  Travel demand model is not calibrated against travel speed/time  Traffic is not routed appropriately  Overestimate average travel speed

6. VDF Estimation Study Design - Foundamental Thoughts The VDF should be:  Well Behaved – reaction to the changes of travel demand, traffic controls and cross-streets  Simple – computation time  Convex – model convergence  Least Data Demanding - implementation Data Collected must cover whole range of congestion

7. VDF Estimation Study Design – Data Collection Method  Floating-Car method with portable GPS devices  Two major arterial corridors were selected Corridor Name Area TypeLength (Mile) # of Lanes# of Signalized Intersections Broadway Blvd Central Urban 76(4)18 Ina RdSuburban449  Survey Duration 3 weekdays (Mar. 3 – 6, 2008), 12 hours a day (6:00AM – 6:00PM) Data collected from Broadway Blvd to estimate the model; data collected from Ina Rd to validate the model

8. VDF Estimation Collected Data  GPS 1(2)-Sec Vehicle Location Data

9. VDF Estimation Collected Data  Distance between signalized intersections  Posted speed limits  Lane Configuration for each street segment between intersections  15-min interval traffic counts between major intersections Collected concurrently at 7 locations on Broadway Blvd and 3 locations on Ina Rd  Signal phasing/timing/coordination information Collected from jurisdictions

10. VDF Estimation VDF Model Form - Percentage of through traffic - Traffic Progression Adjustment Factor - Coefficients - Segment capacity - Intersection Approach Capacity for through traffic - signal g/c ratio for through traffic - midblock free-flow travel time, NCHRP 387 Signal Delay (NCHRP 387) BPR function Adjustment based on congestion - Signal Cycle Length

11. VDF Estimation Nature of the function form  Convex (when Beta’s >= 1) Convex g/c ratio Midblock congestionIntersection congestion  Sensitive to Signal Timing & Congestion

12. VDF Estimation Parameters  Capacity Mid-block - HCM approach - (Linkclass, AreaType) lookup Table Intersection - Saturation rate 1800/1900 vehicle/hr/lane (HCM) - Signal g/c ratio  Speed NCHRP Report 387 High-speed facilities (>= 50 mph) Low-speed facilities (< 50 mph) Or

13. VDF Estimation Parameters  Through Traffic Percentage (70%-90%)  Traffic Progression Adjustment Factor - HCM 2000 (0 – 2.256) - NCHRP Report 387 ConditionProgression Adjustment Factor Uncoordinated Traffic Actuated Signals0.9 Uncoordinated Fixed Time Signals1.0 Coordinated Signals with Unfavorable Progression 1.2 Coordinated Signals with Favorable Progression 0.9 Coordinated Signals with Highly Favorable Progression 0.6

14. VDF Estimation Model Estimation – Prepare Dataset  Identify the floating car locations and arrival times immediately after the intersections to compute travel time and travel distance for each run  Build the dataset with one record for each pair of identified travel distance and travel time between two neighboring intersections  Append the following data to each record in the dataset Traffic Counts Street Segment Capacity Free-Flow-Speed Signal Cycle Length Signal g/c Ratio Signal Traffic Progression Adjustment Factor Intersection Saturation Rate

15. VDF Estimation Model Estimation – Regression  Nonlinear regression Often no global optimum…  Regression Methods - Enumeration Method (Least Square)  Specify range & increment for each parameter  Enumerate the combinations of possible values for each parameter  Compute MSE for each combination of parameter values  Save 50 combinations of the parameter values that result in the least MSE - Statistical Analysis Software (SPSS, SAS)  Verify the parameters estimated from Enumeration Method  Report statistical significance for estimated parameters

16. VDF Estimation Model Estimation – Results  Enumeration Method Best_Alpha1Best_Beta1Best_Alpha2Best_Beta2 Best_MSE 1.9 2.12.4464.9736023 1.71.82.12.4464.97755 1.61.72.12.5465.0029037 222.12.3465.0132826 1.8 22.4465.0143812 21.922.4465.0149071 1.8 2.12.5465.0155575 1.81.92.12.3465.0163662 2.12 2.4465.0249737 1.9 22.3465.0272314 2.1222.3465.0363844 ……………

17. VDF Estimation Model Estimation – Results  Statistical Analysis Software (SPSS & SAS)  Both Methods reported very similar parameter estimates ParameterEstimateStd. Error 95% Confidence Interval Lower BoundUpper Bound a1 1.835 (1.9).890.0893.581 b1 1.858 (1.9).535.8092.907 a2 2.073 (2.1).2131.6552.491 b2 2.392 (2.4).4751.4603.324 Parameter Estimates R 2 = 0.38

18. VDF Validation  Ina Rd Data Apply the parameters estimated from Broadway Blvd data to Ina Rd Corridor NameAverage I-I Travel Time (Sec) RMSE (Sec) % RMSE Broadway Blvd5321.540% Ina Rd6727.8 (26.9) 41.5% (40.2%)

19. VDF Validation  Average Regional Travel Speed Parkway Major Arterial Minor Arterial Frontage Road Average SPEED51.045.546.845.346.1 BPR – FFS from NCHRP Report 387 BPR – FFS from PAG Model Speed Lookup Table New VDF – FFS from NCHRP Report 387 Parkway Major Arterial Minor Arterial Frontage Road Average SPEED36.932.035.729.533.5 Parkway Major Arterial Minor Arterial Frontage Road Average SPEED51.045.546.845.340.9

20. VDF Validation  Travel Times of Individual Routes RouteTravel Time (min)Travel Distance (mile) Actual Number of Signalized Intersections Modeled number of Signalized Intersections ReportedModel Estimated (BPR) Model Estimated (New VDF) 1351731122624 211610496 330142592125 4211319.591715 5401931132322 N W E NE N

21. VDF Implementation  New VDF is made with C codes and compiled as the modeling software DLL  OUE Assignment is used to replace standard UE assignment for faster convergence  FAQs Q: Posted Speed Limits for future year network A: Use the average of the present similar facilities in terms of link class and area type Q: Cycle Length, g/c Ratio, Progression Adjustment Factor for future year network A: Categorize the intersection in terms of the facility type of intersecting streets, area type and so on

22. Conclusions  Empirical Model Provide some insights into the traffic dynamics, but not as much as HCM traffic flow/congestion models  Report more precise vehicle travel time/speed  Reasonably sensitive to intersection configuration Turning traffic may experience further delay that is not captured by the VDF  Further study with more samples is necessary (in plan)  Other function forms should be investigated

23. Questions, Comments Or Suggestions? Aichong Sun Email: asun@pagnet.orgasun@pagnet.org Kosok Chae Email: kchae@pagnet.orgkchae@pagnet.org Tel: (520) 792-1093