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


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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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


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Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

The SCAG Highway Network


The scag highway network network l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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)


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Ontario EMME/2 Users' Group Meeting

Toronto, April 2005]

Adjustment factors


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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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

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 l.jpg

Ontario EMME/2 Users' Group Meeting

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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:


Slide25 l.jpg

Ontario EMME/2 Users' Group Meeting

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Slide26 l.jpg

Ontario EMME/2 Users' Group Meeting

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Assignment ResultsAM truck volume by class


Conclusions l.jpg

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


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Ontario EMME/2 Users' Group Meeting

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