Estimating Link Travel Time with Explicitly Considering Vehicle

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

Content Outline I. Current Status of VDF in Travel Demand Model II. VDF Estimation III. VDF Validation IV. VDF Implementation V. Conclusions

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

Current Status of VDF in Travel Demand Model VDF Considering Intersection Delay q Logit-based Volume Delay Function Israel Institute of Transportation Planning & Research q HCM Intersection Delay Function q 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 q q Function are not convex in nature No convergence for traffic assignment procedure

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

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

VDF Estimation Study Design – Data Collection Method q Floating-Car method with portable GPS devices q Two major arterial corridors were selected Corridor Name Area Type Length (Mile) # of Lanes # of Signalized Intersections Broadway Blvd Central Urban 7 6(4) 18 Ina Rd Suburban 4 4 9 Data collected from Broadway Blvd to estimate the model; data collected from Ina Rd to validate the model q Survey Duration 3 weekdays (Mar. 3 – 6, 2008), 12 hours a day (6: 00 AM – 6: 00 PM)

VDF Estimation Collected Data q GPS 1(2)-Sec Vehicle Location Data

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

VDF Estimation VDF Model Form Signal Delay (NCHRP 387) BPR function Adjustment based - Percentage of through traffic on congestion - 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 Cycle Length

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

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

VDF Estimation Parameters q Through Traffic Percentage (70%-90%) q Traffic Progression Adjustment Factor - HCM 2000 (0 – 2. 256) - NCHRP Report 387 Condition Progression Adjustment Factor Uncoordinated Traffic Actuated Signals 0. 9 Uncoordinated Fixed Time Signals 1. 0 Coordinated Signals with Unfavorable Progression 1. 2 Coordinated Signals with Favorable Progression 0. 9 Coordinated Signals with Highly Favorable Progression 0. 6

VDF Estimation Model Estimation – Prepare Dataset q Identify the floating car locations and arrival times immediately after the intersections to compute travel time and travel distance for each run q Build the dataset with one record for each pair of identified travel distance and travel time between two neighboring intersections q 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

VDF Estimation Model Estimation – Regression q Nonlinear regression Often no global optimum… q 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

VDF Estimation Model Estimation – Results q Enumeration Method Best_Alpha 1 Best_Beta 1 Best_Alpha 2 Best_Beta 2 Best_MSE 1. 9 2. 1 2. 4 464. 9736023 1. 7 1. 8 2. 1 2. 4 464. 97755 1. 6 1. 7 2. 1 2. 5 465. 0029037 2 2 2. 1 2. 3 465. 0132826 1. 8 2 2. 4 465. 0143812 2 1. 9 2 2. 4 465. 0149071 1. 8 2. 1 2. 5 465. 0155575 1. 8 1. 9 2. 1 2. 3 465. 0163662 2. 1 2. 4 465. 0249737 1. 9 2 2. 3 465. 0272314 2. 1 2 2 2. 3 465. 0363844 … … …

VDF Estimation Model Estimation – Results q Statistical Analysis Software (SPSS & SAS) Parameter Estimates R 2 = 0. 38 95% Confidence Interval Parameter Estimate Std. Error Lower Bound Upper Bound a 1 1. 835 (1. 9) . 890 . 089 3. 581 b 1 1. 858 (1. 9) . 535 . 809 2. 907 a 2 2. 073 (2. 1) . 213 1. 655 2. 491 b 2 2. 392 (2. 4) . 475 1. 460 3. 324 q Both Methods reported very similar parameter estimates

VDF Validation q Ina Rd Data Apply the parameters estimated from Broadway Blvd data to Ina Rd Corridor Name Average I-I Travel Time (Sec) RMSE (Sec) % RMSE Broadway Blvd 53 21. 5 40% Ina Rd 67 27. 8 (26. 9) 41. 5% (40. 2%)

VDF Validation q Average Regional Travel Speed BPR – FFS from NCHRP Report 387 Parkway Major Arterial Minor Arterial Frontage Road Average SPEED 51. 0 45. 5 46. 8 45. 3 46. 1 BPR – FFS from PAG Model Speed Lookup Table Parkway Major Arterial Minor Arterial Frontage Road Average SPEED 51. 0 45. 5 46. 8 45. 3 40. 9 New VDF – FFS from NCHRP Report 387 Parkway Major Arterial Minor Arterial Frontage Road Average SPEED 36. 9 32. 0 35. 7 29. 5 33. 5

VDF Validation q Travel Times of Individual Routes Route Travel Time (min) Reported Model Estimated (BPR) Model Estimated (New VDF) Travel Distance (mile) Actual Number of Signalized Intersections Modeled number of Signalized Intersections N 1 35 17 31 12 26 24 W 2 11 6 10 4 9 6 E N 3 30 14 25 9 21 25 4 21 13 19. 5 9 17 15 NE 5 40 19 31 13 23 22

VDF Implementation q New VDF is made with C codes and compiled as the modeling software DLL q OUE Assignment is used to replace standard UE assignment for faster convergence q 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 future year network A: Categorize the intersection in terms of the facility type of intersecting streets, area type and so on

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

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