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Transportation Modeling ApproachDirect vs. Sequence

Meeghat Habibian

Modeling

approach

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(1) the direct approach.

MODELING APPROACHES

(2) the sequenced choice model approach. sequencing a series of models of choice and then combining them

a direct application of the concepts of microeconomic demand modeling

Approaches in travel demand modelingApproaches in travel demand modeling

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(1) the direct approach.

MODELING APPROACHES

(2) the structured choice model approach.

predicting the number of trips made in an urban area as a function of demand and supply characteristics

Approaches in travel demand modelingApproaches in travel demand modeling

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The Direct Approach:The Direct Approach:

The following attributes need to be identified:

1 purpose

2 origin

3 destination

4 mode

5 route

6 time of day

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X pijmrt

the number of trips made by an individual during a given

period of time, p=purpose, origin=i, destination=j, mode=m,

route =r, and at time of day= t

demand function:

all the attributes of all the alternatives simultaneously

The Direct Approach:The Direct Approach:

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Dp = vector of demand variables for trip purpose p

S ijmrt = vector of supply variables for trips with attributes

given by i, j, m, r and t

The Direct Approach:The Direct Approach:

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the total number of variables in the demand function:

d + ijmrt

In the quite realistic situation when d = 3, i= 3, j= 5,

M = 3, R = 2, and T =3,

the number would be 273

The Direct Approach:The Direct Approach:

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Simplifications in the Direct Approach models:Simplifications in the Direct Approach models:

Elimination of the cross-elasticities of demand for different

trip purposes, p, which has been assumed.

Eliminating the t index and constructing demand functions

for trips over all time periods (i.e., typical weekday).

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Simplifications in The Direct Approach models:

Another level of simplification is when origins and

destinations are left in the model (*aggregation on route and

modes), resulting in the origin-destination demand model or

a generation-distribution model:

The extreme of such a simplification is when all attributes

are suppressed except the trip origin or

a trip-generation model:

Simplifications in the Direct Approach models:Simplifications in the Direct Approach models:

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Example of The Direct Approach:Example of The Direct Approach:

One of the earliest direct demand models for an urban freeway

bridge in the San Francisco Bay Area, The Kraft-Wohl model

(1967) :

Trip volume

purpose

time of day

income measure

Population measure And …

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The Sequenced Choice Approach:The Sequenced Choice Approach:

The Direct Approach:

All the attributes of all the alternatives simultaneously

The Sequenced Choice Approach:

The number of trips is first decided, and then the other

attributes .

Sequential process

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Sequenced Choice

Approach

UTPS

Reversemodeling

The Sequenced Choice Approach Methods:

Two methods which are different in modeling trip generation

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The first method in sequence approach (UTPS)The first method in sequence approach (UTPS)

This method is common in practice:

Urban Transportation Planning System (UTPS)

A trip-generation model is defined Xpi, then distributed

among the alternatives available for mode, destination and

route choices, using models of travel choice.

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UTPS process:

trip-generation model

Mode spilt Assignment

distributing among the available destinations

Urban Transportation Planning System (UTPS)Urban Transportation Planning System (UTPS)

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The total travel demand is not elastic with respect to the

attributes of the supply system and that trips are generated

on the basis of demand variables only.

Attempts to correct this are made by either incorporating

aggregate measures of supply in the trip-generation model

(e.g., accessibility index)

UTPS major drawback

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proportion of all trips, that would select

route r route choice function

vector of supply

variables

set off all roads available

for this i,j,m

The second method in sequence approach (Reverse modeling)The second method in sequence approach (Reverse modeling)

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Using previous, provide a:

weighted average of the supply characteristics

modeling the conditional choice of mode:

Mode choice function

Reverse Modeling

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The weighted average of the supply characteristics to any

destination can be obtained:

The destination choice model can now be based on these

weighted supply values:

Destination choice function

Reverse Modeling

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the weighted average of all supply value from i:

a trip-generation demand model can be specified:

Reverse Modeling

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A transportation system serving an area:

1Purposea given trip purpose

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3

4

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originOne origin

Destination3 possible destinations

Modetwo modal networks

Routetwo routes

time of day--------------

Reverse Modeling example

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The travel times on

the network

The travel costs on

the network vector of

destinations

attractiveness

Reverse Modeling example

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Amounts of traffic flows from an origin i to destinations j by

each of the modes and routes?

The hierarchy assumed is, destination choice is first, and using that,

the choice of mode is made on the basis of which route is chosen .

1-modeling the choice of route conditional on mode choice:

Reverse Modeling example

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bases route choice only on travel times

Invariant respect to route

Reverse Modeling example

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Reverse Modeling example

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1- choice of route conditional on mode choice:

2-calculation of weighted average travel time for each mode

and destination combination:

Reverse Modeling example

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2-

for example: t11=(25)(0.39)+(16)(0.61)=19.51≈20 t12=(36)(0.4)+(24)(0.6)=28.8≈30

Reverse Modeling example

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3- A logit mode choice model:

Where V(m, j) is a linear choice of travel time & cost:

Reverse Modeling example

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3- computation of The weighted average values of the time

and cost functions Vˆ(j) for each destination:

Vˆ(j)=Σm V(m,j) p(m│j)

5.19=(5)(0,62)+(5.5)(0.38)

Reverse Modeling example

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4- A gravity destination choice model:

5- calculating p(m,r,j) matrix:

Stage 4

Stage 3

Stage 1

Reverse Modeling example

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5-

Reverse Modeling example

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6-Trip generation

measure of generalized transport cost

Xi =681

Reverse Modeling example

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7-allocating 681 trips among all the modes, routes, and

destinations according to the p(j,m,r) matrix

Reverse Modeling example

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1- choice of route conditional on mode choice.

2-calculation of weighted average travel time for each mode. and

destination combination.

3- modeling mode choice (a logit) .

4- modeling destination choice (a gravity).

5- calculating p(m,r,j) matrix.

6-computing Trip generation.

7-allocating all trips among all the modes, routes, and destinations .

Example summary