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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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michael florian shuguang he inro solutions
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]

multi class assignment cars and trucks
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…
multi class assignment cars and trucks the reality
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
volume delay functions and pce
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
application
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
slide6
Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

The SCAG Highway Network

the scag highway network network
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
six classes of demand
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
trip tables for the highway assignment
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

a delay study was carried out meyer and mohades
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.
slide11
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)

slide12
Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

Adjustment factors

slide13
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

slide14
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

slide15
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

slide16
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

slide17
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

slide18
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

slide19
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

slide20
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

slide21
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)

slide22
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

slide23
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.
measures of convergence
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:
slide26
Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

Assignment ResultsAM truck volume by class

conclusions
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
regular slide
Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

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Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

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Ontario EMME/2 Users' Group Meeting

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