Introduction to Large Scale Modeling Systems
Cinzia Cirillo, Ph.D., Associate Professor
Department of Civil and Environmental Engineering
University of Maryland
Sept 3rd, 2013
Heart 2013 – Summer School
Stockholm
About myself
• MS Civil Engineering
Universita “Federico II” – Naples (ITALY)
• PhD Transportation Engineering
Politecnico di Torino – Torino (ITALY)
• Stagiare and Consultant
Hague Consulting Group The Hague (NL) and Cambridge (UK)
• Post Doc – Marie Curie fellowship (EU)
Applied MATH - University of Namur (BELGIUM)
• Assistant and now Associate Professor (with tenure)
Department of Civil and Environmental Engineering
University of Maryland (USA)
• This year on sabbatical leave at TU-Delft (NL)
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My students at UMD…
(Pratt, Michael, JM, Nayel, Renting, Me, Yangwen)
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Table of Contents
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Terminology
Four-step models
Tour-based models
Activity-based models
Integrated land use and transportation models
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Terminology of Network Representation
• Zones (Centroid, Centroid Connectors)
• Nodes
• Links
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Four-Step Trip-Based Travel Demand Model
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What are the Four Steps?
• Trip Generation (Ti) – Number of trips produced in and attracted to zone
“I” [Number of trips that will be generated]
• Trip Distribution (Tij) – Number of trips produced in zone “i” and attracted
to zone “j” [Where the trips might go]
• Mode Split (Tijm) – Number of trips produced in zone “i” and attracted to
zone “j” traveling by mode “m” [Which mode of transportation do
travelers choose – automobile, rail, bus, bicycle, etc.]
• Traffic Assignment (Tijmr) – Number of trips produced in zone “i” and
attracted to zone “j” traveling by mode “m” over route “r” [Predicts the
path the trips will take]
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Trip Generation Model: Terminology
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Trip
Trip Ends
Tours
Home-Based Trip
Non-Home-Based Trip
Trip Production
Trip Attraction
Trip Generation
Trip Purpose
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Methods for Trip Generation Modeling
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Growth Factor Analysis
– Often used for external trip generation modeling
Cross Classification Methods
– Most widely used in current practices
Regression Models
– Zone-level regression
– Household level regression
Combining Cross-Classification and Regression Methods
Trip Rate Analysis
– Often used for special trip generators
– ITE Trip Generation Manual
Matching Trip Generations and Attractions
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Cross Classification Models
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Zone-Level Regression Analysis: Example
Pi = 22.4 + 1.87HHi + 0.22Ai
Aj = 57.2 + 0.87Ej + 0.15Rj
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Production
Attraction
Pi: Total number of HBW trips produced from zone i
Aj: Total number of HBS trips attracted to zone j
HHi: Total number of households in zone i
Ai: Total number of automobiles in zone i
Ej: Total employment in zone j
Rj: Total retail space in zone j
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Matching Productions and Attractions
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Pi: number of trips produced from zone i
Aj: number of trips attracted to zone j
P’i adjusted number of trips produced from zone i
A’j: adjusted #trips attracted to zone j
i, j: index of zones
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Methods for Trip Distribution Modeling
• Growth Factor Analysis
– Use it only if there are no other better feasible method
• Synthetic Model (e.g. Gravity Model)
– Most widely used in practice
• Discrete Choice Model
– More flexible model structure and behaviorally rich
– Gravity model can be shown as a special case of discrete choice model
• Statistical/Optimization Methods for Estimating OD Trip Tables from
Traffic Counts
• Intervening Opportunity Model
• Etc.
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Basic Gravity Model
• Idea comes from Newton’s Law of Gravitation
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Where:
Tij: Number of trips from to Pi: Productions at i
Aj: Attractions at j
Fij: A function of travel time, distance, and/or cost
– e.g. Fij = 1/(Cij)2 , or Fij = exp(b*Cij)
• Kij: Socioeconomic factor (specified by the modeler)
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Model Choice
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Decision maker
Alternatives
Attributes of alternatives
Decision rule
– Conjunctive rules, e.g. Satisfaction
– Disjunctive rules, e.g. A set of if-then rules
– Lexicographical rules, e.g. Dominance
– Compensatory rules, e.g. Utility maximization
– Combination of rules, e.g. Elimination by aspects
– Other Heuristic Decision Rules
– Etc
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Utility Maximization Theory
U1n = U(t1n, c1n) = b1t1n + b2c1n
U2n = U(t2n, c2n) = b1t2n + b2c2n
• Individual n chooses alternative 1 if U1n>U2n
• When there are multiple alternatives, individual n chooses alternative 1 if
U1n > Uin of all other alternatives.
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Random Utility Maximization Theory
U1n = U(t1n, c1n) = b1t1n + b2c1n + e1n
U2n = U(t2n, c2n) = b1t2n + b2c2n + e2n
Let
V1n = b1t1n + b2c1n
V2n = b1t2n + b2c2n
U1n = V1n + e1n
U2n = V2n + e2n
V: Systematic utility
e: Random utility
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Discrete Choice Models
• Binary:
Prob (1) = P(U1 > U2)
= P (V1n + e1n > V2n + e2n)
= P (e2n – e1n < V1n – V2n )
• Multinomial: Prob (i) = P(Ui > Max Uj,j≠i)
• If e is assumed to be normally distributed, a Probit choice model is
obtained.
• If e is assumed to be logistically distributed, a Logit choice model is
obtained.
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Traffic Assignment / Equilibrium
Supply: Travel cost = f (Travel demand)
Demand: Travel demand = f (Travel cost)
• An equilibrium is achieved when both supply and demand equations are
simultaneously satisfied
• Wardrop’s Two Traffic Equilibrium Principles
– First Principle: User Equilibrium (UE)
Each user acts to minimize his/her own travel cost. At UE, all used
routes between each OD pair have equal travel costs, while all unused
routes have higher travel costs.
– Second Principle: System Optimal (SO)
Each user acts to minimize the total travel cost in the system. At SO,
the lowest total system travel cost is achieved.
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Classification of Traffic Assignment
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Tour-Based and Activity-Based Models
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Activity-Based Models Recognize…
• Travel is a derived demand
• Spatial, temporal, transportation and interpersonal interdependencies
constrain activity/travel behavior
• Household and other social factors/structures influence travel and activity
behavior
Activity-based approaches aim at predicting which activities are conducted
where, when, for how long, with whom, the transport mode involved and
ideally also the implied route decisions.
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Typical Specification of ABM: Type 1
• Population synthesis and updating
• Mobility-lifestyle choices (auto, home location etc.)
• Day-level activity pattern generation (List of Activities with or without
sequencing)
• Scheduling of activities
• Activity or tour-based mode and destination choices
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Typical Specification of ABM: Type 2
• Population synthesis and updating
• Mobility-lifestyle choices (auto, home location etc.)
• Day-level activity pattern generation (Primary and secondary tours and
their sequencing)
• Tour-level primary activity destination, mode, and scheduling choices
• Stop-level secondary activity destination, mode, and scheduling choices
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ABM History
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HATS (Jones 1979)
CARLA (Jones et al. 1983)
STARCHILD (Recker et al. 1986a, 1986b)
SCHEDULER (Garling et al. 1989)
SMASH (Ettema et al. 1993)
SAMS and AMOS (Kitamura et al. 1993, RDC Inc. 1995, Kitamura et al. 1996)
MIDAS (Kitamura and Goulias 1989, Goulias and Kitamura 1996)
SMART (Stopher et al. 1996)
GISICAS (Kwan 1997)
PCATS (Kitamura and Fujii 1998)
ALBATROSS (Arentze and Timmermans 2000)
PETRA (Fosgerau 2001)
SIMAP (Kulkarni and McNally 2001)
TASHA (Miller and Roorda 2003)
CEMDAP ( Bhat et al. 2004)
FAMOS (Pendyala et al. 2004)
TRANSIMS (Los Alamos National Laboratory 2005)
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ABM in Practice
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U.S.
– Atlanta, GA
– Boston, MA
– Columbus, OH
– Dallas, TX
– Denver, CO
– New York, NY
– Portland, OR
– Sacramento, CA
– San Francisco, CA
– Southeast Florida
– Statewide in Oregon
International
– Netherlands
– Swiss
– Germany
– Chile
– Etc
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ABM Benefits
• Predicts travel behavior along a continuous time axis and scheduling
adjustments;
• Assesses the impact of sophisticated travel demand management measures;
• Can be easily modified to evaluate policy scenarios with or without new SP
surveys (e.g. extended transit service, dynamic pricing, daycare facilities at
work, flexible work hours);
• Produces results with desired level of spatial and temporal accuracy using
synthetic population sample;
• More comprehensively evaluates the impact of transportation projects and
policies on the entire activity-travel pattern not trip travel pattern, just on a
trip.
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ABM Data Needs
• Demand Side
– Longitudinal and geographic information on household or individual
time use (e.g. type of activities, travel, activity locations, activity
duration, scheduling);
– Socio-demographic information (e.g. household composition, age,
gender, job, income, housing);
– Auto-ownership and other household mobility and lifestyle choices;
– Activity-travel pattern changes/shifts over time and in response to
transportation system changes;
– Household characteristics with regard to telecommunication.
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ABM Data Needs
• Supply Side
– Transportation networks coded to the activity-stop level; • Level of
service of the transportation network by time of day (this could be
endogenous with DTA);
– Daily, day-of-the-week, and seasonal activity time windows (e.g. store
open hours, periods during which specific activities can be pursued);
– Spatial and non-spatial inventory of activity locations, land use, and
economic data.
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ALBATROSS (Arentze and Timmermans 2000, 2004)
• Albatross: A learning based transportation oriented simulation system
• The model predicts which activities are conducted when, where, for how
long, with whom and also transport mode
• Decision tree is proposed as a formalism to model the heuristic choice
• Considers various constraints on behavior:
– Situational constraints: can’t be in two places at the same time
– Institutional constraints: such as opening hours
– Household constraints: such as bringing children to school
– Spatial constraints: e.g. particular activities cannot be performed at
particular locations
– Time constraints: activities require some minimum duration
– Spatial temporal: constraints an Spatial-individual cannot be at a
particular location at the right time to conduct a particular activity
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ALBATROSS (Arentze and Timmermans 2000, 2004)
• Albatross assumes that choice behavior is based on rules that are formed
and continuously adapted through learning while the individual is
interacting with the environment (reinforcement learning) or
communicating with others (social learning).
• Options for rule-based behavior representation:
– Decision trees (used in Albatross)
– Classification rules
– Bayesian network
– Etc.
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Albatross Model Flowchart
Each oval
represents a
decision
tree
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CEMDAP (Bhat et al. 2003)
• CEMDAP: Comprehensive Econometric Micro-simulator for Daily
Activity-travel Patterns”
• A system of econometric models that represent the activity-travel decisionmaking behavior of individuals.
• Input: Various land-use, socio-demographic, activity system, and
transportation level-of-service attributes
• Output: Complete daily activity-travel patterns for each individual in the
household.
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Daily Activity-Travel Pattern: Worker
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Daily Activity-Travel Pattern: Non-Worker
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CEMDAP Modeling Framework
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Activity Generation-Allocation Module
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Activity Generation-Allocation Models
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Pattern/Tour/Stop-Level Scheduling Modules
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Pattern/Tour/Stop-Level Scheduling Models
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Activity-Based Model Applications
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Effects of development patterns on travel behavior
Sensitivity to price and behavioral changes
Effects of transportation system and system condition
Need for improved validity and reliability
Ability to evaluate policy initiatives
Better analysis of freight movement
Ability to show environmental effects
Modeling low-share alternatives
Better ability to evaluate effects on specific subgroups
Reflect non-system policy changes (TDM, ITS)
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Transportation Eras and Urban Growth Patterns
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Integrated land use and transportation models
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Population Density vs. Distance to City Center
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Population Density vs. %Transit Mode Share
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Transportation and Land Use
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A More Detailed Theoretical Framework
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Land Use Model Components
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Input: Total population and total employment by type in the study area
Output: Population and employment by type in each spatial analysis unit
Typical Spatial Analysis Unit: TAZ, Census tract, Parcel, Block, Grid cell
Demand Modules: Household location choice, Employment location
choice, and/or Household/employment relocation choice
• Supply Modules: Housing development, business real estate development
• Balancing Supply and Demand: No balancing, Price and equilibrium,
Disequilibrium
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Land Use-Transportation Microsimulation
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UrbanSim
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The Travel/Activity
Scheduler for
Household Agents
(TASHA) model
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Thank you!
Q&A
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Integrated Discrete Continuous Choice Models
Theory and Applications
Household Vehicle Ownership, Type and Usage
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Table of Contents
1. Introduction
2. Methodology
3. Case Study
4. Conclusions
5. Future Work
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Introduction
Methodology
Case Study
Conclusions
Future Work
Motivation
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In the U.S., transportation contributes approximately 27 percent of total greenhouse
gas emissions. 71 percent of the oil consumption directs to fuels used in
transportation, in which 40 percent is used to fill up gasoline tanks in our personal
vehicles.
The American households are highly dependent on private vehicles – in 2009, the
average vehicle ownership per household is 2.05, and there are only about 5% of
the households who do not have a car.
The use of private vehicles has strong relationship with traffic congestion, energy
consumption and our environment.
Therefore, it is very crucial to understand the people’s behavior on the wheels,
particularly, how many vehicles they own, the types of the vehicles and how many
miles they travel.
In fact, households make those decisions simultaneously. As transportation
modelers, we’d better to estimate the decisions in one system, in stead of separately,
in order to best understand their travel behavior hence provide better reference for
the policy makers.
However, in the literature there are only a few studies that investigated the three
choices jointly.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Literature Review
• Discrete-continuous models derived from conditional indirect utility
function (i.e., Train, 1986)
– In the discrete part, the utilities of the alternatives are represented by
conditional indirect utility functions, and the person will choose the alternative
with the highest utility.
– In the continuous part, the demand functions are derived from the conditional
indirect utility functions by using Roy’s identity property.
• Limitations:
– The models estimate the choice probabilities and the demand equations
sequentially, not simultaneously .
– The estimates are consistent but not as efficient as full information maximum
likelihood, because the unobserved component of utility and the error in the
demand equation generally contain some common unobserved factors.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Literature Review (Con’t)
• Multiple Discrete Continuous Extreme Value (MDCEV) model
• Limitations:
– Does not include vehicle holding decision.
– Requires fine classification of vehicles as one type of vehicle cannot be chosen
twice by the household.
– The assumption of fixed total mileage budget for every household implies that
it is not possible to predict changes in the total number of miles in response to
policy changes.
– There is only a single error term underlying both discrete and continuous
choices.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Literature Review (Con’t)
• Bayesian Multiple Ordered Probit and Tobit (BMOPT) Model
• Limitations:
– The computation becomes intensive for a large number of vehicle categories, as
the number of equations to be estimated increases proportionally with the
number of vehicle types.
– Ordered mechanism may not perform as well as unordered mechanism in
modeling car ownership decisions (Bhat and Pulugurta, 1998; Potoglou and
Kanaroglou, 2008)
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Introduction
Methodology
Case Study
Conclusions
Future Work
Research Objectives
• Develop a mathematical framework to model the household choices on
vehicle ownership, the types and annual mileage traveled; in particular, the
model should be able to
– simultaneously estimate discrete (vehicle holding and types) and
continuous (vehicle usage) decision variables;
– take into account a large number of alternatives in both the vehicle
holding and the vehicle type choices;
– have no budget on the mileage traveled;
– capture the correlations of the unobserved factors between the discrete
and continuous parts;
– have flexible specifications; and
– be sensitive to policy analysis.
• In addition, investigate the performance of ordered and unordered
structures in discrete-continuous models.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Unordered Discrete-Continuous Model
Number of vehicles
& the type of each
Household
0
1 - Type1
2 - Type1 & Type2
3 - Type1 & Type2 & Type3
4 - Type1 & Type2 & Type3 & Type4
Annual miles traveled
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Introduction
Methodology
Case Study
Conclusions
Future Work
Unordered Discrete-Continuous Model (Con’t)
• In the unordered structure, the household is assumed to be rational and to
choose the alternative of vehicle ownership level that maximizes its utility.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Unordered Discrete-Continuous Model (Con’t)
• The discrete choices Y – Multinomial Probit
Where,
• The continuous choice Yreg– Regression
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Introduction
Methodology
Case Study
Conclusions
Future Work
Unordered Discrete-Continuous Model (Con’t)
• The integrated discrete-continuous model:
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Introduction
Methodology
Case Study
Conclusions
Future Work
Unordered Discrete-Continuous Model (Con’t)
• Estimation with Monte Carlo Simulation:
• Where
is a draw from a multivariate normal with mean
and variance
• Then, the final Simulated Log Likelihood of the model is:
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Introduction
Methodology
Case Study
Conclusions
Future Work
Unordered Discrete-Continuous Model (Con’t)
• Estimation with Numerical Computation (Genz ,1992):
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Introduction
Methodology
Case Study
Conclusions
Future Work
Ordered Discrete-Continuous Model
• The ordered response structure uses latent variables to represent the vehicle
ownership propensity of the household.
• Suppose two latent variables yd and yr represent the preference levels for
vehicle holding and vehicle usage:
• The number of vehicles holding by the household (Y ) is determined by the
value of latent variable yd, specifically:
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Introduction
Methodology
Case Study
Conclusions
Future Work
Ordered Discrete-Continuous Model (Con’t)
• Similarly, in order to jointly to capture the correlation between the discrete
and continuous parts, we allow the error terms to be correlated. Thus, the
error terms follow a bivariate normal distribution:
• The likelihood of one observation is
• Where
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Introduction
Methodology
Case Study
Conclusions
Future Work
Ordered Discrete-Continuous Model (Con’t)
• Tthe conditional mean and variance of ordered probit are:
• The final likelihood of one observation can be written as:
• where,
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Introduction
Methodology
Case Study
Conclusions
Future Work
Case Study
• Data sources:
– 2009 National Household Travel Survey (NHTS) data – 1420
observations in the Washington D.C. Metropolitan area
– Vehicle characteristics
• Choice set:
– Vehicle holding: 0, 1, 2, 3 and 4 car(s)
– Vehicle type: 120 alternatives for the type choice of each vehicle (12
classes x 10 vintages)
– Vehicle usage: annual miles traveled
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12 classes of vehicle for each 10 vintages—Total of 120 alternatives
The classes of vehicles are
– small domestic car;
Subsample of chosen
alternative plus 20
– compact domestic car;
randomly selected ones
– mid-size domestic car;
– large domestic car;
– luxury domestic car;
– small import car;
– mid-size import car;
– large import car;
– sporty car;
– minivan/van;
– pickup trucks;
– SUVs.
The 10 vintages are pre-1999 and the years 2000 through 2008.
Introduction
Methodology
Case Study
Conclusions
Future Work
Case Study (Con’t)
• Data Statistics
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Introduction
Methodology
Case Study
Conclusions
Future Work
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Introduction
Methodology
Case Study
Conclusions
Future Work
Estimations of Vehicle Type Sub-models
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Introduction
Methodology
Case Study
Conclusions
Future Work
Estimations of Vehicle Type Sub-models (Con’t)
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Introduction
Methodology
Case Study
Conclusions
Future Work
Model Estimations
unordered discrete-continuous unordered discrete-continuous
model with simulation
model without simulation
Same as Model 2 except
Ordered discreteno logsum (utility from the
continuous model
type choices)
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Introduction
Methodology
Case Study
Conclusions
Future Work
Model Estimations (Con’t)
*Note: Model 1 is the unordered discrete-continuous model with simulation; Model 2 is the unordered discretecontinuous model with numerical computation; Model 3 is the ordered discrete-continuous model; Model 4 is
the same as Model 2 except excluding the "logsum" variable, which make it comparable to Model 3.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Model Estimations (Con’t)
1 car
2 cars
3 cars
4 cars
Mileage
1 car
2 cars
3 cars
4 cars
Mileage
1 car
2 cars
3 cars
4 cars
Mileage
1 car
2 cars
3 cars
4 cars
Mileage
#cars mileage
1 car
#cars
mileage
2 cars 3 cars 4 cars Mileage
1 car
2 cars
3 cars
4 cars
Mileage
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Introduction
Methodology
Case Study
Conclusions
Future Work
Model Applications
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Introduction
Methodology
Case Study
Conclusions
Future Work
Model Applications (Con’t)
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Introduction
Methodology
Case Study
Conclusions
Future Work
Conclusions
• Developed an integrated discrete continuous choice model to
simultaneously estimate the household choices on vehicle ownership
(discrete), the types (discrete) and annual mileage traveled (continuous).
• The model is able to include a large number of alternatives in both the
vehicle holding and the vehicle type choices.
• The model allows unrestricted correlations of the unobserved factors
between the discrete and continuous parts.
• The model accommodates flexible specifications.
• There is no budget constraint in the mileage traveled.
• The model can be applied for policy analysis.
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Introduction
Methodology
Case Study
Conclusions
Future Work
Conclusion (Con’t)
• The case study for the Washington D.C. Metropolitan area is based on the
latest national dataset – 2009 NHTS
• The preliminary results show that
– the model gives reasonable estimates of the coefficients;
– the covariance matrix well explains the correlations between the
unobserved factors from the utilities of the discrete choices and the
demand function of the continuous choice;
– the non-simulation approach provides better model fit;
– the performance of the model is improved if the information about
vehicle type choice is included;
– the unordered discrete continuous model is more appropriate in
estimating household vehicle ownership and usage decisions, than the
ordered discrete continuous model .
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