A Peek inside the New Black Box:

A Peek inside the New Black Box:A Peek inside the New Black Box:

Understanding the Methodology of Understanding the Methodology of Knoxville’s New Accessibility-Based ModelKnoxville’s New Accessibility-Based Model

A Peek inside the New Black Box:A Peek inside the New Black Box:

Understanding the Methodology of Understanding the Methodology of Knoxville’s New Accessibility-Based ModelKnoxville’s New Accessibility-Based Model

Vince Bernardin, Jr., Ph.D.Vince Bernardin, Jr., Ph.D.Bernardin, Lochmueller & Associates, Inc.Bernardin, Lochmueller & Associates, Inc.

Vince Bernardin, Jr., Ph.D.Vince Bernardin, Jr., Ph.D.Bernardin, Lochmueller & Associates, Inc.Bernardin, Lochmueller & Associates, Inc.

Knoxville’s “Accessibility-based” Model Overview and notable features

Core methodology developed at Northwestern Motivation Understanding the problem The current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

Knoxville’s “Accessibility-based” ModelKnoxville’s “Accessibility-based” Model Overview and notable featuresOverview and notable features

Core methodology developed at Northwestern Motivation Understanding the problem The current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

March 12, 2009

Methodology1. A hybrid disaggregatedisaggregate / aggregateaggregate system

To maximize model fidelity and minimize run time

A New, Alternative Model Design

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Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice

Activity / TourGeneration

PopulationSynthesizer

Accessibility

Travel Times

LinkFlows

Departure TimeChoice

Variables Models

Disa

ggregate M

odelsA

ggregate M

odels

Vehicle AvailabilityChoice

Example of Aggregation Bias

Consider mode choice 100 households with an average of 2.2 cars per

household 5 households with no cars5 households with no cars, 15 hh with one car,

50 hh with two cars, 20 hh with three cars, 5 hh with four cars, 5 hh with five

The full-information disaggregate picture looks a lot different than the aggregate picture of the same the same scenarioscenario – because aggregation entails information loss.

March 12, 2009



2.2. Disaggregate vehicle & tour mode choicesDisaggregate vehicle & tour mode choices

3.3. Departure time choiceDeparture time choice


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Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels


Vehicle Availability ORL Choice Model Each individual household chooses how

many vehicles to own / lease No aggregation bias Vehicle ownership levels respond to

Demographics (household size, income, number of workers, students, etc.)

Gas PricesGas Prices Transit AvailabilityTransit Availability Urban Design Urban Design (pedestrian environment

/ grid vs. cul-de-sac design)

No Veh

1 Veh

Nest

Nest

Root

2 Veh

Nest

3 Veh

4+ Veh

Choice Hierarchy

In traditional four-step models, mode choice was modeled conditional on (after) destination choice (due to a preoccupation with choice riders and commuting).

Instead, we modeled stop location or destination choice conditional on (after) mode choice

March 12, 2009

Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels


Choice Hierarchy

In traditional four-step models, mode choice was modeled conditional on (after) destination choice (due to a preoccupation with choice riders and commuting).

Instead, we modeled stop location or destination choice conditional on (after) mode choice We sequentially estimated combined (nested logit) combined (nested logit)

mode and stop location (and sequence) choice modelsmode and stop location (and sequence) choice models And all the logsum / nesting parameters were in the

acceptable ranges without using constraintswithout using constraints, suggesting that this may be the correct choice hierarchy

Choice Hierarchy

This reverse choice hierarchy reflects the fact that many travelers are more likely to change many travelers are more likely to change destinations than switch modesdestinations than switch modes Even for work tours, the data suggests that in

Knoxville, people are more likely to change jobs than change their travel mode to work

This may not be as unreasonable as it seems, considering captive riderscaptive riders, dependent on the bus to get to work

Imposing the traditional hierarchy traditional hierarchy may be a source of “optimism bias” “optimism bias” in transit forecasts

Departure Time Choice

Demand by 15-minute intervals based on: Travel time during period (peak-spreadingpeak-spreading) , and Bias variables interacted with sinusoidal functions:

Origin / Destination Accessibilities (urban vs. rural) Return factor (ratio of employment to population at origin

vs. destination) SOV vs. HOV trip

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2.2. Disaggregate vehicle & tour mode choiceDisaggregate vehicle & tour mode choice


4. Feedback of ACCESSIBILITYACCESSIBILITY as well as travel time 1. To introduce sensitivity to ‘lower level’ choices in

‘upper level’ decisions


March 12, 2009

Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels


Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels


Travel Cost Elasticity Found elasticities of out-of-home activities with

respect to accessibility of 0.13 - 0.16 Lower tour-making by residents of ruralrural (lower-

accessibility) areas, Decreased tour/stop-making in response to

congestioncongestion (decreased accessibility), Induced tour/stop-making in response to added added

network capacitynetwork capacity (increased accessibility), Induced tour/stop-making in response to new land new land

use developmentsuse developments in other nearby zones (increased accessibility)

Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels


Residence Effects on Trip Length

When people choose their residence location, they also choose how far they are willing to travel.

We allowed travelers’ willingness-to-travel, and hence, trip lengths to vary as a function of the accessibility of their residence location The willingness-to-travel of residents of the most urban most urban

(most accessible) areas was about 10% lower 10% lower than the regional average

The willingness-to-travel of residents of the most rural most rural (least accessible) areas was about 200% higher 200% higher or twice the regional average for most activity types

Cost Elasticity from Accessibility

Including accessibility in both activity generation and stop location choice reflects fewerfewer, but longerlonger ruralrural tours; more shorter urban more shorter urban tours

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2.2. Disaggregate tour mode choiceDisaggregate tour mode choice


4. Feedback of ACCESSIBILITYACCESSIBILITY as well as travel time 1. To introduce sensitivity to ‘lower level’ choices in

‘upper level’ decisions

5. A ‘double destination choicedouble destination choice’ framework1. Produce trips consistent w/ tours & tour cost minimization


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Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels



Core methodology developed at NorthwesternCore methodology developed at Northwestern MotivationMotivation Understanding the problem The current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

Motivation

Trip distribution or destination choice is the largest source of errorlargest source of error in traditional travel models (Zhao & Kockelman, 2002)

Gravity models typically explain only about 20%-30%20%-30% of the variation in destination choices

Why are the models so bad? Assumption all travelers behave the same Lack of data (prices, parking, etc.) Assumption that these unobserved Assumption that these unobserved

variables are distributed randomlyvariables are distributed randomly Assumption all destination choices are Assumption all destination choices are

independent (no trip-chaining)independent (no trip-chaining)

Motivation Trips do not form closed tours

– physically impossible!physically impossible!

Trips are distributed inconsistently with tour cost minimization – behaviorally implausiblebehaviorally implausible

Existing solutions are costly


Core methodology developed at Northwestern Motivation Understanding the problemUnderstanding the problem The current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

Understanding the Problem

Two-fold problem with four-step spatial distributions Open tours Insensitivity to tour costs

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An example of a possible trip table from a gravity model with seven trips (H-a, H-c, a-H, a-c, b-b, b-c, c-c): There is no way that all seven of these trips can be arranged

into one or more tours. Real travelers could not produce the travel pattern

in this trip table, but a four-step model can! For instance, one traveler doesn’t return home!

Open Tours H a b c

H 0 1 0 1 2

a 1 0 0 1 2

b 0 0 1 1 2

c 0 0 0 1 1

1 1 1 4 7

ab

H

c

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Stops Locations (trip ends) which Minimize Tour Costs: Will be closer to home (radial dimension) Will be closer to each other (angular dimension)

In the Four-Step Model: Home-based trips minimize radial costs, but minimize radial costs, but NOTNOT angular angular Non-home-based trips minimize angular costs, but minimize angular costs, but NOTNOT radial radial

Tour Cost Minimization

H

a

bd

ef

z

x

y

c

Non-home-based Trips The four-step approach represents the

distribution of non-home-based trips as the result of a singlesingle gravity (destination choice) model

But NHB trips involve two destinations, so at least twotwo destination or stop location choices are needed


Core methodology developed at Northwestern Motivation Understanding the problem The current solutionThe current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

The Traditional (Sequential) Solution

Proposed by Shiftan (1998), used in all tour / activity-based models in U.S.

a

H

bATT = Hb+ba-Ha c

ATT = Hc+ca-Ha

The New Problem

Building tours sequentially Requires computationally intensive simulation Takes as many steps as stops Results in long model run times!


Core methodology developed at Northwestern Motivation Understanding the problem The current solution A new solutionA new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

A New Simultaneous Solution

First choose stop locations (where to go)Then choose how to sequence them (where to

go from)a

H

b

c

Network

TAZ

Flow Averaging

TrafficAssignment

HOV and TollChoices

Stop SequenceChoice

Stop LocationChoice

Tour ModeChoice



Accessibility

Travel Times

LinkFlows


Variables Models

Disa

ggregate M

odelsA

ggregate M

odels


A New Simultaneous Approach

Advantage:Advantage: only two steps regardless of how many stops = fast run times!

Challenge 1:Challenge 1: how to insure that sequences form closed tours?

Challenge 2:Challenge 2: how to include the cost of non-home-based trips in the choice of stop locations?

a

H

b

c


Core methodology developed at Northwestern Motivation Understanding the problem The current solution A new solution The Traveler Conservation ConstraintThe Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental results

Agenda

Traveler Conservation Constraint Requiring that whoever goes in, comes

out results in consistency with tours

,hij hj hj hj hjki k

T D T O T h j H a b c

f 0 5 0 3 8

g 1 1 0 3 5

H 22 33 11 11 77

a 1 4 0 2 7

4 13 1 9 27

H a b c

H 0 1 1 0 22

a 2 0 0 1 33

b 0 1 0 0 11

c 0 1 0 0 11

22 33 11 11 77

Shadow Prices The aggregate application allows the

enforcement of the constraint by iterative shadow pricing, following Andrew Stryker’s method for doubly constraining destination choice

ln ln

| ln ln

hj hj c ij

hj hj c ij

s D c

j hi s D c

j

eP

e

11

hjn nhj hj n

hiji

Ts s

T

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An example of a possible trip table with a Traveler Conservation Constraint for seven trips (H-a, H-b, a-H, a-H, a-c, b-a, c-a): These trips could be produced by either the tours

H-a-H & H-b-a-c-a-HH-a-H & H-b-a-c-a-H H-b-a-H & H-a-c-a-HH-b-a-H & H-a-c-a-H

It can be proved that any trip table with identical row and any trip table with identical row and column sums is consistent with some set of tours.column sums is consistent with some set of tours.

Closed Tours H a b c

H 0 1 1 0 22

a 2 0 0 1 33

b 0 1 0 0 11

c 0 1 0 0 11

22 33 11 11 7

a

b

H

c

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An example of a possible trip table from “forced symmetry” with a pathological tour The traveler could not make the pathological tour b-c-b because

they never visit b or c

The double destination choice framework minimizes The double destination choice framework minimizes this.this.

The probability of a pathological tour is related to the difference between the probability that the traveler will visit a subset of stops and the probability that the traveler will visit that subset of stops from home

Pathological Tours

h a b c

h 0 2 0 0 22

a 2 0 0 0 22

b 0 0 0 1 11

c 0 0 1 0 11

22 22 11 11 6

a

b

H

c

Under-determination of ToursIn general, there are far more possible

tours than (independent) trip probabilities, so the probabilities of tours cannot be determined from this model alone without further assumptions.

The approach is fastfast because it produces trips consistent with tours without determining the tours, themselves.

2

1

2 1S

s

s

Z Z Z


Advantage:Advantage: only two steps regardless of how many stops / tours = fast run times!



a

H

b

c


Core methodology developed at Northwestern Motivation Understanding the problem The current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location ChoiceTrip-Chaining Effects in Stop Location Choice Experimental results

Agenda

Stop Location ChoiceGravity Model

Stewart (1941), Huff (1963), Wilson (1967) Based on a single impedance (time from

home/origin) and employment / attractions Still most widely used (TRB, 2007)Still most widely used (TRB, 2007)

MNL Destination choice models Academic research (Ben-Akiva, 1973;

Lerman, 1976; Koppelman, 1977, 1978)

Recent applications in practice(Chow et al., 2005; Jonnalagadda et al., 2001)

Mostly traveler heterogeneity

Limitations of Standard MethodsBoth gravity and more general MNL models are

independent of the spatial arrangement or accessibility of alternative destinations

B

A

B

h

Scenario 1 Scenario 2

C

A

h

C

Independence

In traditionaltraditional models, two equidistantequidistant, equal-sizeequal-size destinations are equally probableequally probable.

What about Accessibility?

What if one is more accessiblemore accessible to other possible destinations?

ComplementarityMaybe the more accessiblemore accessible one is more probable -

because you have to go a nearby destination anyway, and so it’s convenient.

Higher accessibility means the expected costexpected cost of a possible

subsequent trip is lower.

Accessibility in Destination Choice

In 1984, Kitamura used an accessibility variable to incorporate trip-chainingtrip-chaining effects in destination choice





a

H

b

c

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But, maybe the less accessibleless accessible is more probable because half the time you go the other direction,

you go to a nearby alternative instead.

Substitution

Accessibility in Destination Choice

In 1984, Kitamura used an accessibility variable to incorporate trip-chainingtrip-chaining effects in destination choice

The prior year, Fotheringham used an accessibility variable to incorporate differential spatial competition differential spatial competition in destination choice

More recently,Bhat & collaborators have found one or the other in different cases

Different FindingsFotheringham finds substitutionsubstitution effects

Prob(C) in Scenario 1 >> Prob(C) in Scenario 2

Kitamura finds complementaritycomplementarity effectsProb(C) in Scenario 1 << Prob(C) in Scenario 2

B

A

B

h

Scenario 1 Scenario 2C

A

h

C

SubstitutionSubstitution and ComplementarityComplementarity

In some situations, only one effect may be present or dominate Fotheringham studied mostly migration and

long-distance travel where trip-chaining trip-chaining effects are neglegible

In other cases, both may be present but Kitamura / Fotheringham’s Competing Destinations (CD) models only capture a net effect

ACDC Models (Bernardin, Koppelman & Boyce, 2009)

Agglomerating and Competing Destination Choice (ACDC) Models Use 2 types2 types of accessibility:

Accessibility to complementscomplements (other places you need to go, regardless)

Accessibility to substitutessubstitutes (other places you might go, instead) ln

| ln

j c hjS

ASC

AC j

CAC j

j

Sh Sc A jj j

AS A

j AA

c

h S c

j

eP

e

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ACDC Models attempt to minimize both dimensions of tour costs: Stops will be closer to homecloser to home (radial dimension) Stops will be closer to each othercloser to each other (angular dimension)

Tour Costs

H

a

bd

ef

z

x

y

c

ln ln

| ln ln

Sj AS j AC jk k

k

Sj AS j AC j k k

k

S A d B e

j h S A d B e

j

eP

e

βC

βC

c

c

β

β

c jkh

jc j k

j

h

c

c





a

H

b

c


Core methodology developed at Northwestern Motivation Understanding the problem The current solution A new solution The Traveler Conservation Constraint Trip-Chaining Effects in Stop Location Choice Experimental resultsExperimental results

Agenda

Estimation ACDC stop location choice model

parameters were estimated From year 2000 household survey data for

Knoxville, Tennessee Using a genetic algorithm Based on Maximum Likelihood

With feasibility constraintsc<0, '<0, 'C<0, 'S<0 and AC>0

Estimation Results Multiple optima were observed

At least a local optimum was always found within the feasible region

HBM

-7419

-7418

-7417

-7416

-7415

-7414

-7413

-7412

-7411

-3 -2.5 -2 -1.5 -1 -0.5 0

alphas

log

like

liho

od

Home-Based Maintenance ACDC CD-PA CD Gravity (MNL)

Variable Parameter t stat

Parameter t stat

Parameter t stat

Parameter t stat

Attraction / Size / Quantity Variables

Retail Employment 3.1240 29.7 3.0896 29.5 3.0147 28.8 3.1569 29.6

Service Employment 1 1 1 1

THETA 1 1 1 1

Quality Variables

Average Travel Time (AVGTT) -0.25820.2582 -48.3 -0.25370.2537 -49.5 -0.2516-0.2516 -48.6 -0.26070.2607 -47.2

Accessibility to All Attractions -0.21500.2150 -13.2 -1.3044-1.3044 -10.9

- AVGTT in Accessibility -1.4389 *

Accessibility to Complements 0.82550.8255 6.6

- AVGTT in Acc. to Complements -0.4951 *

Accessibility to Similar -0.86050.8605 -9.3

- AVGTT in Acc. to Substitutes -0.9622 *

Log Likelihood at Convergence: -6666.20 -6683.62 -6703.57 -6761.00

Log Likelihood at Zeros: -9437.78 -9437.78 -9437.78 -9437.78

Rho Squared w.r.t. Zeros: 0.294 0.292 0.290 0.284

* Note: t-statistics were not calculated for embedded parameters since the significance of these effects should be evaluated by the parameter on the accessibility main effects.

ACDC Home-based Maintenance

Home-Based Other ACDC CD-PA CD Gravity (MNL)

Variable Parameter t stat

Parameter t stat

Parameter t stat

Parameter t stat

Attraction / Size / Quantity Variables

Population 1.6327 6.8 1.2983 5.9 1.3905 6.3 1.4524 7.3

Enrollment 1.2443 4.0 1.2134 4.1 1.2468 4.0 1.3061 4.5

Retail Employment 2.9590 14.1 3.1100 15.2 3.1265 14.8 3.1582 15.3

Service Employment 1 1 1 1

THETA 1 1 1 1

Quality Variables

Avgerage Travel Time (AVGTT) -0.2198-0.2198 -40.9 -0.21950.2195 -40.8 -0.2191-0.2191 -40.6 -0.2192-0.2192 -40.5

Accessibility to All Attractions -0.0251-0.0251 -1.5 -0.09500.0950 -0.6

- AVGTT in Accessibility -2.2885 *

Accessibility to Complements 8.19768.1976 3.9

- AVGTT in Acc. to Complements -1.3988 *

Accessibility to Similar -8.3318-8.3318 -3.9

- AVGTT in Acc. to Substitutes -1.3822 *

Log Likelihood at Convergence: -5428.78 -5438.22 -5439.16 -5439.35

Log Likelihood at Zeros: -7091.66 -7091.66 -7091.66 -7091.66

Rho Squared w.r.t. Zeros: 0.234 0.233 0.233 0.233

* Note: t-statistics were not calculated for embedded parameters since the significance of these effects should be evaluated by the parameter on the accessibility main effects.

ACDC Home-based Other

Forecasting Resulting probabilities from ACDC models

estimated with 2000 data were compared against new 2008 data.

ACDC models outperformed gravity models in forecasting even more than in the base year ACDC model offered 3.5%3.5% improvement improvement over the

explanatory power of gravity for HBM in 2000 ACDC model offered 6.7%6.7% improvement improvement

over the explanatory power of gravity for HBM in 2008

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Policy Analysis & Planning

What happens if a newnew development occurs?

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In current models, all the other destinations get equally less probable.


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Complements get moremore probable – new trips to old destinations!

In ACDC models, nearby destinations are affected more than distant ones.


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Sensitivity Analyses – Real World Examples

Comparison of gravity and ACDC models for three new developments to illustrate spatial competition and trip-chaining effects. A new factorynew factory employing 1,000 workers in Loudon county

indirectly attracts 125 daily non-work stops to the county.

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Sensitivity Analyses Loudon County factory’s effect on shopping stops

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Comparison of gravity and ACDC models for three new developments to illustrate spatial competition and trip-chaining effects. A new factorynew factory employing 1,000 workers in Loudon county

indirectly attracts 125 daily non-work stops to the county. A new Food Citynew Food City with 105 employees indirectly attracts a

NET 27 (+55-28) daily trips to nearby zones (halo effect)

Sensitivity Analyses – Real World Examples

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Sensitivity Analyses New Food City’s effect on shopping stops

There’s no oneone “right” way of modeling travel behavior for every region.

There are a variety of different advanced model designs each with different pros and cons. This approach has some advantages, in terms of computational computational

efficiency efficiency / run time, And it allows incremental improvements incremental improvements from existing models But it probably works best in a semi-aggregatesemi-aggregate model

The ‘double destination choice’ framework allows for a new set of options for model designs.

Some Closing Thoughts

Thank You!

A Peek inside the New Black Box:

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