Paul Metaxatos Urban Transportation Center University of Illinois at Chicago

1. Some Issues in Transportation Demand Modeling and ITS Deployment Planning Paul Metaxatos Urban Transportation Center University of Illinois at Chicago CTS-IGERT – Weekly Seminar May 14, 2009

2. Some Computational Considerations In Transportation Demand Modeling

3. The Gravity Model

4. Estimation Procedures DSF ML Estimation

5. O-D Distance Measures • Straight-line (Euclidean) distance • Travel distance • Travel time • Generalized cost • Functional distance • Taxonomical distance

6. 1 Mode – 1 Commodity – 1 Travel Time Parameter – National Level Geography Size of Origin – Destination Table (Cells) Size of ML Estimation Problem (I+J+1) – System of Equations Storage Requirements 50 states 2,500 101 20 KB of RAM 3141 counties 9,865,881 6,283 ~ 78 MB of RAM 33,000 zip codes 1,089,000,000 66,001 ~ 8 GB of RAM 65,000 census tracts 4,225,000,000 130,001 ~ 33 GB of RAM

7. Covariance Matrices M – the coefficient matrix of the right-hand side of

8. Geography Size of Origin – Destination Table (Cells) Size of Covariance Matrix – (I*J, I*J) cells Storage Requirements 50 states 2,500 6,250,000 50 MB of RAM 3141 counties 9,865,881 97,335,607,906,161 ~ 778 TB bytes of RAM 33,000 zip codes 1,089,000,000 1,185,921,000,000,000,000 ~ 9 EB of RAM 65,000 census tracts 4,225,000,000 17,850,625,000,000,000,000 ~ 142 EB of RAM 1 Mode – 1 Commodity – 1 Travel Time Parameter – National Level

9. Two Applications In Transportation Demand Modeling

10. 5115 Study • Measure the ton-miles and value-miles of international • trade traffic carried by highway for each State • Evaluate the accuracy and reliability of such measures • for use in the formula for highway apportionments

11. Small-Area Estimation of O-D Flows

12. Trip Generation and Small Household Travel Surveys (HTS)

13. Number of Workers Household Size 1 2 3 4+ 0 6.28 (53) 9.22 (40) 16.00 (3) 8.00 (3) 1 6.09 (87) 10.42 (45) 10.94 (18) 9.06 (15) 2 - (-) 9.56 (46) 10.81 (11) 15.46 (28) 3 - (-) - (-) 11.00 (2) 11.83 (6) 4 - (-) - (-) - (-) 10.66 (3) Issues with Small HTS and Trip Generation Average Number of Trips per Household (number of households in parenthesis) • Unusual observations • Small number of observations • No observations -: indicates category not possible in this classification.

14. Unusual Observations • Problem • Outliers • Influential observations • Remedy • Examine diagnostics from equivalent regression problem

15. Small Number of Observations • Problem • Reliability of trip generation rates • Remedy • CART analysis • - non-parametric • - binary recursive partitioning algorithm

16. CART Example Using Two Independent Variables Number of Workers Household Size 1 2 3 4+ Number of Workers Household Size 0 6.28 (53) 9.22 (40) 11.67 (21) 8.89 (18) 1 2 3 4+ 1 6.09 (87) 10.42 (45) 0 6.28 (53) 9.22 (40) 16.00 (3) 8.00 (3) 2 - - 9.56 (46) 10.85 (13) 15.46 (28) 1 6.09 (87) 10.42 (45) 10.94 (18) 9.06 (15) 3 - - - - 11.44 (9) 2 - (-) 9.56 (46) 10.81 (11) 15.46 (28) 4 - - - - - - 3 - (-) - (-) 11.00 (2) 11.83 (6) 4 - (-) - (-) - (-) 10.66 (3) Before CART After CART Average Number of Trips per Household (number of households in parenthesis) Average Number of Trips per Household (number of households in parenthesis) -: indicates category not possible in this classification. -: indicates category not possible in this classification.

17. Another CART Example Trip Purpose Household Size Trip Purpose Household Size 1 2 3 4+ 1 2 3 4+ HB-Work Number of cases 1.90 71 2.43 70 2.60 25 2.64 36 HB-Work Number of cases 1.94 171 2.33 223 2.72 79 HB-Shop Number of cases 1.64 42 2.26 76 2.50 20 2.81 32 HB-Shop Number of cases HB-School Number of cases 2.19 58 2.26 23 1.22 9 2.72 11 HB-School Number of cases HB-Other Number of cases 2.44 93 4.00 105 3.97 29 6.14 47 HB-Other Number of cases 2.44 93 4.00 105 4.22 58 6.15 47 NHB Number of cases 2.82 99 3.61 107 4.48 29 4.61 41 NHB Number of cases 2.83 99 3.62 107 4.61 41 Before CART After CART Trip Rates by Household Size and Trip Purpose Trip Rates by Household Size and Trip Purpose

18. Trip Rates by Household Size, Number of Workers and Trip Purpose (after CART Analysis)

19. Trip Rates by Household Size, Number of Workers and Vehicle Availability (after CART Analysis)

20. Number of Workers Household Size 1 2 3 4+ 0 6.28 (53) 9.22 (40) 16.00 (3) 8.00 (3) 1 6.09 (87) 10.42 (45) 10.94 (18) 9.06 (15) 2 - (-) 9.56 (46) 10.81 (11) 15.46 (28) 3 - (-) - (-) 11.00 (2) 11.83 (6) 4 - (-) - (-) - (-) 10.66 (3) Row-column Decomposition Analysis As an Imputation Method Average Number of Trips per Household (number of households in parenthesis) -: indicates category not possible in this classification.

21. Row-column Decomposition Analysis As an Imputation Method (cont.) Step 1: Column Means Subtracted Step 2: Row Means Subtracted • *U - unavailable • Examples • Column fit = means of column; • e.g., 6.18=(6.28+6.09)/2 • Cell value = observed value – column fit; • e.g., 0.10=6.28-6.18 Examples Row effect = mean of step one row; e.g., 0.10=(0.10-0.51+3.81-3.00)/4 Residuals = cell value of step one – row effect; e.g., -0.00=0.10-0.10 Grand mean = mean of column fits; e.g., 9.78=(6.18+9.73+12.19+11.00)/4 Column effect = column fit – grand mean; e.g., -3.60=6.18-9.78 Original cell value = grand mean + row effect + column effect + residual; e.g., 6.28=9.78+0.10-3.60-0.00

22. Row-column Decomposition Analysis (cont.) Logarithmic Transformation of Trip Rates

23. COMPUTER ASSISTED SCHEDULING AND DISPATCHING SYSTEMS IN PARATRANSIT

24. CASD Scenario Hardware Software Centralized One central server serves all operators One statewide system Decentralized One server per operator One or more different systems Regional One server per region One or more different systems Alternative CASD Deployment Scenarios

25. Centralized Approach

26. Advantages • Facilitates centralized coordination at the state level • Lower software costs • Disadvantages • Need for reliable Internet connections • Fear of loosing control of services and operations

27. Decentralized Approach

28. Advantages • Offers strong local control • No need for high speed Internet connections • Disadvantages • More on-site technical support • Possibility of multiple standards • Difficult to coordinate among multiple providers • Increased ownership costs

29. Regional Approach

30. Advantages • Little worry about maintaining and updating software and • hardware • Facilitates monitoring of contract performance by State DOT • Facilitates implementation of brokerage • Proximity to client facilitates maintenance, training and service • of client software • Disadvantages • Communication needs less than centralized but more than • decentralized approaches

31. Focus Group Overall Findings • Centralized approach too difficult for smaller agencies • Fear of loosing control triggers desire to as much • decentralization as possible • Decentralized approach is most desired but with • standardization • Fear of half-way implementation • State DOT should pay for software, hardware, implementation, • technical support, contractual support with vendor

32. Cost Analysis – Summary of Findings • The cost of a decentralized implementation for a typical • agency was about $65,000 (first year) and • $25,000 annually thereafter (2000 dollars) • The respective costs for the regional approach were about • $60,000 initially and $18,000 annually thereafter • Regional approach could potentially save more than • $10,000 per agency per year on average. • This amounts to more than $300,000 savings per year • for the 30 (5311) providers in Illinois