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Trip Table Estimation from Counts. Transportation leadership you can trust. Science or Magic?. presented to 12th TRB National Planning Applications Conference Houston, TX presented by Dan Beagan Cambridge Systematics, Inc. May 18, 2009. Science vs. Magic.

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Trip Table Estimation from Counts


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trip table estimation from counts

Trip Table Estimation from Counts

Transportation leadership you can trust.

Science or Magic?

presented to12th TRB National Planning Applications ConferenceHouston, TX

presented byDan BeaganCambridge Systematics, Inc.

May 18, 2009

science vs magic
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)
science vs magic1
Science vs. Magic

Science

If results are unexpected, the expectations were wrong

Will always duplicate results

Works for believers and non-believers

Magic

  • If results are unexpected, the conditions for the spell weren’t “right”
  • Not expected to duplicate results
  • Works only for believers
transportation planning
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
software packages
Software Packages
  • Caliper TransCAD’s ODME
  • Citilab CUBE ANALYST’s ME
  • PTV VISUM’s TFlowFuzzy
scientific justification trip table estimation from counts
Scientific JustificationTrip Table Estimation from Counts
  • Statistical Principle behind Maximum Entropy
  • Maximum Entropy Techniques in Transportation
  • Applications of Matrix Estimation from Counts
maximum entropy
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
game of dice
Game of Dice

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

trip tables
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 identicalTrip Tables

Job 1

Job 1

Job 1

Larry

Curly

Moe

Larry

Moe

Moe

HOME

HOME

HOME

Job 2

Job 2

Job 2

Curly

Curly

Larry

Job 3

Job 3

Job 3

MICROSTATE 1

MICROSTATE 2

MICROSTATE 3

Job 1

Job 1

Job 1

Curly

Larry

Moe

Curly

Larry

Curly

HOME

HOME

HOME

Job 2

Job 2

Job 2

Larry

Moe

Moe

Job 3

Job 3

Job 3

MICROSTATE 4

MICROSTATE 5

MICROSTATE 6

trip tables maximum entropy
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

9

trip tables maximum entropy1
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

10

fratar growth factor
Fratar Growth Factor
  • For an existing table, Tij, find a new table, tij, given growth targetsoi for the origins anddj 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
a g wilson s gravity model
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

12

logit mode split
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

13

matrix estimation from counts
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

14

od me trip table
(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

15

od me trip table applications
(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

16

od me trip table applications1
(OD)ME Trip Table Applications
  • 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

17

od me trip table applications2
(OD)ME Trip Table Applications

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

18

trip table estimation from counts1

Trip Table Estimation from Counts

Transportation leadership you can trust.

Science or Magic?

presented to12th TRB National Planning Applications ConferenceHouston, TX

presented byDan BeaganCambridge Systematics, Inc.

May 18, 2009