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Assigning mixed traffic of cars and trucks: how to handle asymmetric interactions

Michael Florian, Shuguang He INRO Solutions. Assigning mixed traffic of cars and trucks: how to handle asymmetric interactions. Multi-class assignment : cars and trucks. the usual practice of assigning mixed traffic of cars and trucks is: use the same volume/delay functions;

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Assigning mixed traffic of cars and trucks: how to handle asymmetric interactions

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  1. Michael Florian, Shuguang He INRO Solutions Assigning mixed traffic of cars and trucks:how to handle asymmetric interactions Ontario EMME/2 Users' Group Meeting Toronto, April 2005]

  2. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Multi-class assignment :cars and trucks • the usual practice of assigning mixed traffic of cars and trucks is: • use the same volume/delay functions; • convert the trucks into PCE (or PCU) equivalent numbers by using a conversion factor; • run a multi-class assignment with limitations on the truck sub-network; • the implicit assumption is that the interaction between cars and trucks is symmetric; that is, the conversion factor is constant regardless of traffic conditions, grade, etc…

  3. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Multi-class assignment :cars and trucks - the reality • the actual delay depends on a variety of factors such as the mix of traffic (% trucks), average speed, grade, etc… • the volume delay functions must depend on the mix of trucks and cars and other such factors like the slope of the link • the cost functions are likely to be nonlinear, non-smooth and asymmetric • then, it is necessary to develop a specialized assignment method that can handle such functions

  4. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Volume/delay functions and PCE • VDF (volume delay function). Each class has its own travel time depending on link volume and free speed on the link • PCE (passenger car equivalents). Truck volume is converted to car volume. • Mix of Traffic (congestion factor) • percentage of each class of traffic on the link slope and length of the link by each class

  5. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Application • SCAG region • New macro using emme/2 multi-class assignment with 0 iteration (shortest path) • BPR function: • It uses a look-up table to update PCE’s and delays at every iteration • Step size using a variant of the Method of Successive Averages

  6. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] The SCAG Highway Network

  7. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] The SCAG Highway Network network • Zone: 3325 • 3217 ;SCAG region zone and externals • 108 ;zones converted from parking lots • Regular nodes: 26290 • Directional links: 108897

  8. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Six classes of demand • 1. Passenger cars of one person • 2. Passenger car of two person • 3. Passenger car of three person + • 4. Light-heavy duty trucks, 8500 to 14,000 GVW • 5. Medium-heavy duty trucks, 14,000 to 30,000 GVW • 6. Heavy-heavy duty trucks, over 30,000 GVW

  9. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Trip Tables for the Highway Assignment • Total trips: • drive alone: 5319853; • car pool 2: 1625165; • car pool 3+: 430209 light heavy duty trucks: 85040 • medium heavy duty trucks: 62804 - heavy heavy duty trucks: 38333

  10. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] A delay study was carried out(Meyer and Mohades) • The results of this study are presented in the next slides; • They consist of the computation of PCE equivalents of different trucks depending on traffic mix, length of link and grade.

  11. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Heavy Duty Truck PCE Values ( proportion, length, grade) Heavy Duty Truck PCE Values ( proportion, length, grade)

  12. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Adjustment factors

  13. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE Factors (LH Truck Percent) PCE factors PCE factors Truck percent 0 - 5 Truck percent 5 -10 PCE factors LEGEND LINKL - link length GRADEP - grade percent Truck percent >10

  14. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE factors PCE factors Truck percent 0 - 5 Truck percent 5 -10 PCE factors LEGEND LINKL - link length GRADEP - grade percent PCE Factors (MH Truck Percent) Truck percent >10

  15. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE Factors (HH Truck Percent) PCE factors PCE factors Truck percent 0 - 5 Truck percent 5 -10 PCE factors LEGEND LINKL - link length GRADEP - grade percent Truck percent >10

  16. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE Factors (LH Truck Percent grade) PCE factors PCE factors percent grade 0 - 2 percent grade 3 -4 LEGEND LINKL - link length TRUCKP - truck percent PCE factors PCE factors percent grade > 6 percent grade 5 - 6

  17. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE Factors (MH Truck Percent grade) PCE factors PCE factors percent grade 0 - 2 percent grade 3 -4 LEGEND LINKL - link length TRUCKP - truck percent PCE factors PCE factors percent grade 5 - 6 percent grade > 6

  18. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE Factors (LH Truck Percent) PCE factors PCE factors Truck percent 0 - 5 Truck percent 5 -10 PCE factors LEGEND LINKL - link length GRADEP - grade percent Truck percent >10

  19. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE factors PCE factors Truck percent 0 - 5 Truck percent 5 -10 PCE factors LEGEND LINKL - link length GRADEP - grade percent PCE Factors (MH Truck Percent) Truck percent >10

  20. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE Factors (HH Truck Percent) PCE factors PCE factors Truck percent 0 - 5 Truck percent 5 -10 PCE factors LEGEND LINKL - link length GRADEP - grade percent Truck percent >10

  21. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] PCE factors PCE factors percent grade 0 - 2 percent grade 3 -4 LEGEND LINKL - link length TRUCKP - truck percent PCE factors PCE factors percent grade 5 - 6 percent grade > 6 PCE Factors (HH Truck Percent grade)

  22. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Congestion PCE adjustment Factors PCE adjust factors PCE adjust factors Light heavy duty truck Medium heavy duty truck PCE adjust factors LEGEND v/c - volume/capacity truck percent Heavy heavy duty truck

  23. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Solution Algorithm • Step 0: Initialization. Start with AON assignment based on free flow times; • Step 1: Compute percentage of link flow, v/c ratio and link flow in PCE( look up table); • Step 2: Update travel times; • Step 3: Compute new shortest paths and AON assignments; • Step 4: Compute successiveaverage and update flows; • Step 5: If convergence test not satisfied Go to step 1 ; Otherwise STOP.

  24. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Measures of Convergence • Relative difference between volume at iteration l and successive average volume at iteration l: • Relative gap rgapl between the flow calculated based on • the total travel cost on shortest paths problem network • and the last flow weighted by the current travel time:

  25. Ontario EMME/2 Users' Group Meeting Toronto, April 2005]

  26. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Assignment ResultsAM truck volume by class

  27. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Conclusions • One can perform far more sophisticated multi-class assignments than the standard EMME/2 multi-class assignment; • The computational times compare favourably with the standard EMME/2 multi-class assignment

  28. Ontario EMME/2 Users' Group Meeting Toronto, April 2005]

  29. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Regular slide • optional elaborated title [Outline 1] • heading [Outline 2] • bullet [Outline 3] • sub bullet [Outline 4] • heading [Outline 2] • bullet [Outline 3] • sub bullet [Outline 4]

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  31. Text-image • optional elaborated title [Outline 1] • heading [Outline 2] • bullet [Outline 3] • sub bullet [Outline 4] • heading [Outline 2] • bullet [Outline 3] • sub bullet [Outline 4] Ontario EMME/2 Users' Group Meeting Toronto, April 2005]

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  33. Ontario EMME/2 Users' Group Meeting Toronto, April 2005] Full page object

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