trip dist

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Urban Transportation Planning

Trip Distribution

Urban Transportation Planning 2

Determining P to A Trips

T12

T21

T11

1

3

2


Properties of the P-A Table

Tij Zone 1 Zone 2 Zone 3 Zone 4 Tij = P i Zone 1Zone 2Zone 3Zone 4

Tij = A j


Gravity Model I: Newton

Newtons Law of Gravity

221

d

M M G F =


Gravity Model II: Migration

Intercity Migration after WWII

221

d S S K T =

S 1 and S 2 are sizes of City 1 and City 2


Gravity Model III: Open System

Use Productions and Attractivenesses Constrain Productions

P i are productions in zone i; A j is the attractiveness ofzone j; F ij is the friction factor between zones i and j.

=

k ik k

ij jiij F A F A P T

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Friction Factors I

A friction factor is a measure of proximitybetween two zones.Friction factors are scale independent.

Travel Time

F r i c

t i o n

F a c

t o r


Friction Factors II: Functions

Traditional power function

Exponential function (entropy maximizing)

Gamma function

=ij

t F ij

ij

ij

t ij et F

=

ijt ij e F

=


Friction Factors III: Friction.txt

Table from NCHRP #365Time HBW HBNW NHB

0 100000 100000 1000001 88426 91028 904842 77116 34004 325213 67640 18383 171474 59468 11563 105765 52352 7901 71096 46124 5690 50467 40660 4249 37188 35859 3258 28169 31634 2549 2178

10 27914 2027 1713


SEWRPCs Friction Factors


Reconciling Attractions

If As are defined as attractions, then theprevious equation will not give the correctcolumn totals. Attractiveness values must becalculated to give the expected answer.Typically

Convergence is usually fast .

=

iij

old new T

A A A target


External Stations and the GravityModel

QRS II does not allow trips betweenexternal stations as part of thegravity model.E-E trips must be provided by someother method, perhaps as anAddVTrips.txt file.

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Calibrating Friction Factors I

Compare observed and modeled trip length

distributions. For example, the 9 minutefriction factor needs to be bigger by 12/11.

0

2

4

6

8

10

12

14

1 3 5 7 9 11 13 15 17 19

Time (Minutes)

P e r c e n

t o

f T r i p s

% Trips Model%Trips Observed


Calibrating Friction Factors II

Use a known friction factor function and set

the parameter to give the observed averagetrip length, e.g.,

Select , such that:

ijt ij e F

=

( ) t t = Computed average tr ip length Known average t rip length


Calibrating Friction Factors III

Other calibration methodsChoose from a similar sized city.Use Method II but take average triplength from a similar sized city.Statistically estimate whole frictionfactor function by referencing a knownP-A table from survey data (difficult).


K-Factors

Often called socio-economic adjustmentfactors, but are really fudge factors.

No k factors in QRS II, but P-A times can bemodified by AddHTimes.txt.

=

k ijik k

ijij jiij k F A

k F A P T

Fratar Factoring

Iterative solution method forexpanding an OD table to matchrow and column totals.Applies to any empirical OD table.See Fratar.xls


1

1

Alternative Solution Method


min 1

2

1

2

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Gravity Model Dialog Box

trip dist

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