transportation leadership you can trust. presented to 12th trb national planning applications...

Transportation leadership you can trust.

presented topresented to

12th TRB National Planning Applications Conference12th TRB National Planning Applications ConferenceHouston, TX Houston, TX

presented bypresented by

Dan BeaganDan BeaganCambridge Systematics, Inc.Cambridge Systematics, Inc.

May 18, 2009May 18, 2009

Trip Table Estimation from CountsScience or Magic?

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Science vs. Magic

Any sufficiently advanced technology is indistinguishable from magic

− Arthur C. Clarke, “Profiles of The Future,” (Clarke’s third law)

When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong

− Arthur C. Clarke, “Profiles of The Future”, (Clarke’s first law)

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Science vs. Magic

Magic

If results are unexpected, the conditions for the spell weren’t “right”

Not expected to duplicate results

Works only for believers

Science

If results are unexpected, the expectations were wrong

Will always duplicate results

Works for believers and non-believers

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Transportation Planning

Expected to be based on science

Most methods accepted as scientific

Trip Table Estimation from counts not always accepted

• Method not always understood

–”If you can believe results”

• Method is widely available− Included in standard software packages

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Software Packages

Caliper TransCAD’s ODME

Citilab CUBE ANALYST’s ME

PTV VISUM’s TFlowFuzzy

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Scientific JustificationTrip Table Estimation from Counts

Statistical Principle behind Maximum Entropy

Maximum Entropy Techniques in Transportation

Applications of Matrix Estimation from Counts

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Maximum Entropy

Most probable state is the one with the Maximum Entropy

Statistically, for a given macrostate, the most probable mesostate is the one with the maximum number of microstates

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Snake Snake EyesEyes

Acey Acey DeuceDeuce

Easy Easy FourFour

Fever Fever FiveFive Easy SixEasy Six

Natural Natural or Seven or Seven

OutOut

Acey Acey DeuceDeuce

Hard Hard FourFour



OutOut

Easy Easy EightEight

Easy Easy FourFour

Fever Fever FiveFive Hard SixHard Six


OutOut


Nine Nine (Nina)(Nina)



OutOut

Hard Hard EightEight


Easy Easy TenTen

Easy SixEasy SixNatural Natural

or Seven or Seven OutOut


Nine Nine (Nina)(Nina) Hard TenHard Ten

Yo Yo (Yo-(Yo-

leven)leven)


OutOut



Easy Easy TenTen

Yo Yo (Yo-(Yo-

leven)leven)BoxcarsBoxcars

In “craps” (macrostate)

the most probable roll (mesostate) is a seven, a natural,

because there are more ways (microstates)to make a seven than any other roll

Game of Dice

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The economic impact of three individuals traveling from one home to three geographically different jobs (microstates) may not be the same, but the traffic impact of the trip table (mesostates) is identical

Trip Tables

CurlyCurly

LarryLarry

MoeMoe

CurlyCurly

MoeMoe

LarryLarry

LarryLarry

MoeMoe

CurlyCurly

MoeMoe

CurlyCurly

LarryLarry

MoeMoe

LarryLarry

CurlyCurly

LarryLarry

CurlyCurly

MoeMoe

HOMEHOME HOMEHOME

Job 1Job 1

Job 2Job 2

Job 3Job 3

Job 1Job 1

Job 2Job 2

Job 3Job 3

HOMEHOME

Job 1Job 1

Job 2Job 2

Job 3Job 3

HOMEHOME

Job 1Job 1

Job 2Job 2

Job 3Job 3

HOMEHOME

Job 1Job 1

Job 2Job 2

Job 3Job 3

HOMEHOME

Job 1Job 1

Job 2Job 2

Job 3Job 3

MICROSTATE 1MICROSTATE 1 MICROSTATE 2MICROSTATE 2 MICROSTATE 3MICROSTATE 3

MICROSTATE 4MICROSTATE 4 MICROSTATE 5MICROSTATE 5 MICROSTATE 6MICROSTATE 6

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A solution trip table, t ij, given an existing trip table, T ij , will be a maximum entropy trip table, if the following equation is solved

The solution will depend on the constraints imposed

Trip Tables Maximum Entropy

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Trip Tables Maximum Entropy

Solving for the trip table relies on the following mathematical principles

• The maximum of any monotonically increasing function of tij will have the same solution trip table, tij

• Sterling’s approximation of X !, X ln X – X, is a monotonically increasing function

• LaGrangian multipliers can be used to combine the target and constraint equations

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Fratar Growth Factor

For an existing table, Tij,

find a new table, tij,

given growth targetsoi for the origins and

dj for the destinations

Also known as Furness or IPF, Iterative Proportional Fitting

Choose values for K’i; solve

for K’’j, resolve for K’j;iterate

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A. G. Wilson’s Gravity Model

Traditionally there is no initial table, Tij, so Tij =1

Total cost, C, does not need to be known

Choose values for K’i,

solve for K’’j, then K’i

and iterate

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Logit Mode Split

Traditionally there is no initial Table, Tm, so Tm =1

Indices are modes m for each ij pair

Total utility, U, does not need to be known

Stating the solution as a percentage eliminates the constants

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Matrix Estimation from Counts

A “seed” table, Tij, may be available; otherwise Tij = 1

Constraints exist for those links a which have counts, Va

The probability of traveling between pair ij on link a, pija can be found from assignment scripts

• E.g., for AON, pija = 1 when link a is on the path between i and j

A set of simultaneous equations, which can be solved iteratively, can be developed by substituting the solution into the constraints

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(OD)ME Trip Table

What should you use for the initial trip table?

• Invariant to Uniform Scaling

How many counts and where should they be located?

• Network Sensor Location Problem

How good is the solution?

• Maximum Possible Relative Error

How well does the solution table validate to counts?

• Maximum Entropy

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(OD)ME Trip Table Applications

Subareas

• TAZs are small

• Many traffic counts / turning movements available

• The seed trip table might be disaggregated from a regional travel demand model

• Examples− Traffic Microsimulation OD tables

− Traffic Impact Reports

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Truck tables in TDF Models

• Behavioral based trip table for autos or freight OD table

• Highway network for assignment

• Sufficient link counts for trucks

• Examples− Indiana DOT

− Virginia DOT

− Nashville MPO

− New York City MPO

− Binghamton MPO

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State and multistate models

• No behavioral based trip tables for autos or trucks

• Highway network for assignment

• Sufficient link counts

• Examples− Georgia DOT

− Tennessee DOT

− I-95 Corridor Coalition

− Appalachian Regional Commission

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Questions?

Transportation leadership you can trust.

presented topresented to

12th TRB National Planning Applications Conference12th TRB National Planning Applications ConferenceHouston, TX Houston, TX

presented bypresented by

Dan BeaganDan BeaganCambridge Systematics, Inc.Cambridge Systematics, Inc.

May 18, 2009May 18, 2009

Trip Table Estimation from CountsScience or Magic?

transportation leadership you can trust. presented to 12th trb national planning applications...

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