Methods for large-scale modeling and simulation

Sebastian Hörl

Spring 2023

Université Gustave Eiffel

Overview

  • Lectures covering example sand methods in large-scale transport planning making use of open data sources
     
  • Project work on the assessment of the Grand Paris Express
    • Work in groups of ~5 students
    • Exchange necessary between individual groups
       
  • Assessment
    • Project presentation at the end of the course
    • Short report on the project

Timeline

  • Lectures
    • 10/01 8h30: Examples of large-scale models in transportation
    • 10/01 10h45: Modeling methods I
    • 13/01 14h00: Modeling methods II
    • 13/01 16h45: Introduction to the student project
       
  • Project work
    • 27/01 14h00 + 16h45: Intermediate results
    • 09/02 14h00 + 16h45: Exchange with other groups
    • 23/02 14h00 + 16h45: Final presentation

Timeline

  • Lectures
    • 10/01 8h30: Examples of large-scale models in transportation
    • 10/01 10h45: Modeling methods I
    • 13/01 14h00: Modeling methods II
    • 13/01 16h45: Introduction to the student project
       
  • Project work
    • 27/01 14h00 + 16h45: Intermediate results
    • 09/02 14h00 + 16h45: Exchange with other groups
    • 23/02 14h00 + 16h45: Final presentation

2 weeks

2 weeks

2 weeks

Timeline

  • Lectures
    • 10/01 8h30: Examples of large-scale models in transportation
    • 10/01 10h45: Modeling methods I
    • 13/01 14h00: Modeling methods II
    • 13/01 16h45: Introduction to the student project
       
  • Project work
    • 27/01 14h00 + 16h45: Intermediate results
    • 09/02 14h00 + 16h45: Exchange with other groups
    • 23/02 14h00 + 16h45: Final presentation

IRT SystemX

  • Public/private research institute situated in Paris
     
  • Focus on fostering digital transition in a range of fields from transport, cybersecurity to circular economy
     
  • Transferring research results and tools into active application by development and provision of industry platforms
     
  • Various collaborative projects with multiple French companies (Renault, SNCF, ...) and academic partners (Université Paris Saclay, CentraleSupélec, Université Gustave Eiffel)
     
  • Participation in European projects

http://www.loc.gov/pictures/item/2016800172/

The street in 1900

The street today

https://commons.wikimedia.org/wiki/File:Atlanta_75.85.jpg

  • Autonomous Mobility

  • Mobility as a Service

  • Mobility on Demand

  • Electrification

  • Aerial Mobility

Julius Bär / Farner

The street of tomorrow?

I. Transport simulation

Classic transport planning

  • Zones
  • Flows
  • Peak hours
  • User groups

Aggregated

Agent-based models

0:00 - 8:00

08:30 - 17:00

17:30 - 0:00

0:00 - 9:00

10:00 - 17:30

17:45 - 21:00

22:00 - 0:00

  • Discrete locations
  • Individual travelers
  • Individual behaviour
  • Whole day analysis

Disaggregated

Icons on this and following slides: https://fontawesome.com

MATSim

  • Flexible, extensible and well-tested open-source transport simulation framework
     
  • Used by many research groups and companies all over the world
     
  • Extensions for parking behaviour, signal control, location choice, freight, ...

matsim-org/matsim-libs

MATSim

Synthetic demand

MATSim

Mobility simulation

Synthetic demand

MATSim

Decision-making

10:00 - 17:30

17:45 - 21:00

22:00 - 0:00

Mobility simulation

Synthetic demand

MATSim

Decision-making

Mobility simulation

Synthetic demand

MATSim

Decision-making

Mobility simulation

Analysis

Synthetic demand

https://pixabay.com/en/zurich-historic-center-churches-933732/

II. AMoD in Zurich

https://pixabay.com/en/zurich-historic-center-churches-933732/

Cost structures?

User preferences?

System impact?

Cost Calculator for automated mobility

Stated preference survey

MATSim simulation

1

2

3

What do we know about automated taxis?

What do we know about automated taxis?

Bösch, P.M., F. Becker, H. Becker and K.W. Axhausen (2018) Cost-based analysis of autonomous mobility services, Transport Policy, 64, 76-91

What do we know about automated taxis?

Felix Becker, Institute for Transport Planning and Systems, ETH Zurich.

VTTS

13 CHF/h


 

AMoD

Taxi

19 CHF/h

 

 

Conventional

Car

12 CHF/h
 

 

Public

Transport

AMoD

Car by Adrien Coquet from the Noun Project

Bus by Simon Farkas from the Noun Project

Wait by ibrandify from the Noun Project

VTTS

13 CHF/h
 

 

AMoD

Taxi

19 CHF/h

 

 

Conventional

Car

12 CHF/h
 

 

Public

Transport

 
21 CHF/h

 


32 CHF/h

AMoD

Car by Adrien Coquet from the Noun Project

Bus by Simon Farkas from the Noun Project

Wait by ibrandify from the Noun Project

Model structure

Cost calculator

Plan modification

Discrete Mode Choice Extension

Mobility simulation

Prediction

Price

Trips

- Utilization

- Empty distance, ...

- Travel times

- Wait times, ...

Fleet sizing with dynamic demand

Fleet sizing with dynamic demand

Fleet sizing with dynamic demand

Visualisation

Automated taxi

Pickup

Dropoff

Hörl, S., F. Becker and K.W. Axhausen (2020) Automated Mobility on Demand: A comprehensive simulation study of cost, behaviour and system impact for Zurich

Hörl, S., F. Becker and K.W. Axhausen (2020) Automated Mobility on Demand: A comprehensive simulation study of cost, behaviour and system impact for Zurich

13% reduction in vehicles

100% increase in VKT

Hörl, S., F. Becker and K.W. Axhausen (2020) Automated Mobility on Demand: A comprehensive simulation study of cost, behaviour and system impact for Zurich

100% increase in VKT

Hörl, S., F. Becker and K.W. Axhausen (2020) Automated Mobility on Demand: A comprehensive simulation study of cost, behaviour and system impact for Zurich

Other aspects

Hörl, S., C. Ruch, F. Becker, E. Frazzoli and K.W. Axhausen (2019) Fleet operational policies for automated mobility: a simulation assessment for Zurich, Transportation Research: Part C, 102, 20-32.

Fleet control

Operational constraints

Spatial constraints

Intermodality

Pooling

III. Demand data

https://pixabay.com/en/paris-eiffel-tower-night-city-view-3296269/

Synthetic travel demand

Population census (RP)

Population census (RP)

Income data (FiLoSoFi)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Household travel survey (EDGT)

0:00 - 8:00

08:30 - 17:00

17:30 - 0:00

0:00 - 9:00

10:00 - 17:30

17:45 - 21:00

22:00 - 0:00

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Household travel survey (EDGT)

Enterprise census (SIRENE)

Address database (BD-TOPO)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Household travel survey (EDGT)

Enterprise census (SIRENE)

Address database (BD-TOPO)

Person ID    

Age

Gender

Home (X,Y)

1

43

male

(65345, ...)

2

24

female

(65345, ...)

3

9

female

(65345, ...)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Household travel survey (EDGT)

Enterprise census (SIRENE)

Address database (BD-TOPO)

Person ID    

Activity

Start

End

Loc.

523

home

08:00

(x,y)

523

work

08:55

18:12

(x,y)

523

shop

19:10

19:25

(x,y)

523

home

19:40

(x,y)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Household travel survey (EDGT)

Enterprise census (SIRENE)

OpenStreetMap

GTFS (SYTRAL / SNCF)

Address database (BD-TOPO)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Household travel survey (EDGT)

Enterprise census (SIRENE)

OpenStreetMap

GTFS (SYTRAL / SNCF)

Address database (BD-TOPO)

Synthetic travel demand

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

National HTS (ENTD)

Enterprise census (SIRENE)

OpenStreetMap

GTFS (SYTRAL / SNCF)

Address database (BD-TOPO)

Synthetic travel demand

EDGT

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Enterprise census (SIRENE)

OpenStreetMap

GTFS (SYTRAL / SNCF)

Address database (BD-TOPO)

Synthetic travel demand

Open
Data

Open
Software

+

=

Reproducible research

Integrated testing

National HTS (ENTD)

EDGT

Population census (RP)

Income data (FiLoSoFi)

Commuting data (RP-MOB)

Enterprise census (SIRENE)

OpenStreetMap

GTFS (SYTRAL / SNCF)

Address database (BD-TOPO)

Synthetic travel demand

Open
Data

Open
Software

+

=

Reproducible research

Integrated testing

National HTS (ENTD)

EDGT

Current use cases

Nantes

  • Noise modeling

Current use cases

Lille

  • Park & ride applications
  • Road pricing

Current use cases

Toulouse

  • Placement and use of shared offices

Current use cases

Rennes

  • Micromobility simulation

Current use cases

Paris / Île-de-France

  • Scenario development for sustainable urban transformation
     
  • New mobility services

    Mahdi Zargayouna (GRETTIA / Univ. Gustave Eiffel)
    Nicolas Coulombel (LVMT / ENPC)

Current use cases

Paris / Île-de-France

  • Cycling simulation

Current use cases

Paris / Île-de-France

  • Simulation of dynamic mobility services
     
  • Fleet control through reinforcement learning

Current use cases

Lyon (IRT SystemX)

  • Low-emission first/last mile logistics

Current use cases

Current use cases

Balac, M., Hörl, S., 2021. Synthetic population for the state of California based on open-data: examples of San Francisco Bay area and San Diego County, in: 100th Annual Meeting of the Transportation Research Board. Washington, D.C., January 2021.

Sallard, A., Balać, M., Hörl, S., 2021. An open data-driven approach for travel demand synthesis: an application to São Paulo. Regional Studies, Regional Science 8, 371–386.

Sao Paulo, San Francisco Bay area, Los Angeles five-county area, Switzerland, Montreal, Quebec City, Jakarta, Casablanca, ...

Emissions in Paris

Grand Paris Express

Automated taxis in Paris

Automated taxis in Paris

IV. Logistics

Photo by Tom Fisk from Pexels

Photo by Tom Fisk from Pexels

LEAD Project

Low-emission Adaptive last-mile logistics supporting on-demand economy through Digital Twins

  • H2020 Project from 2020 to 2023
     
  • Six living labs with different innovative logistics concepts
    • Lyon, The Hague, Madrid, Budapest, Porto, Oslo
    • One partner for implementation and one for research each
       
  • Development of a generic modeling library for last-mile logistics scenario simulation and analysis

Lyon Living Lab

  • Peninsula Confluence between Saône and Rhône
     
  • Interesting use case as there are limited access points
     
  • Implementation of an urban consolidation center (UCC) to collect the flow of goods and organize last-mile distribution
    • using cargo-bikes
    • using electric robots
    • and others
       
  • Analysis and modeling through
    • Flow estimation through cameras
    • Simulation of future scenarios
       
  • Focus on parcel deliveries due to data availability

Modeling methodology

Agent-based simulation of Lyon

Demand in parcel deliveries

Distribution by operators

KPI Calculation

  • Main question: What is the impact on traffic and population of implementing an Urban Consolidation Center in Confluence?
     
  • Focus on B2C parcel deliveries due to data availability

Methodology: Parcel demand

Synthetic population

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

Methodology: Parcel demand

Synthetic population

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

Methodology: Parcel demand

Synthetic population

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

Methodology: Parcel demand

Synthetic population

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

Methodology: Parcel demand

Synthetic population

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Iterative proportional fitting (IFP)

  • Based on synthetic population, find average number of purchases delivered to a household defined by socioprofesional class, age of the reference person and household size per day.
\mu_{a,h,s} = d_{s} \cdot \frac{w_{a,h,s}}{365}

Methodology: Parcel demand

Synthetic population

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Maximum entropy approach

  • We now the average number of parcels, but we do not now the distribution of the number of parcels for a household on an average day.
     
  • We know it must be non-negative, and we know the mean.
     
  • Without additional data, we assume maximum entropy distribution, which is Poisson in this case.
F(N \leq n) = \text{Pois}(\mu)

Methodology: Parcel demand

Synthetic population

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Methodology: Parcel demand

Synthetic population

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Methodology: Parcel demand

Synthetic population

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Methodology: Parcel demand

Synthetic population

Gardrat, M., 2019. Méthodologie d’enquête: le découplage de l’achat et de la récupération des marchandises par les ménages. LAET, Lyon, France.

+

Synthetic population

Out-of-home purchase survey
Achats découplés des ménages

Based on sociodemographic attributes of the households, parcels are generated for the city on an average day.

Presence of household members

Methodology: Route optimization

Using a heursitic routing solver, an optimal distribution scheme per distribution center is obtained to arrive at a lower bound estimate for the distance covered for the deliveries.

JSprit

First case study

Hörl, S. and J. Puchinger (2021) From synthetic population to parcel demand: Modeling pipeline and case study for last-mile deliveries in Lyon, Working paper.

Solve VRP-TW based on generated parcels and household presence

JSprit

First case study

Hörl, S. and J. Puchinger (2021) From synthetic population to parcel demand: Modeling pipeline and case study for last-mile deliveries in Lyon, Working paper.

Solve VRP-TW based on generated parcels and household presence

JSprit

Scaling up: City-wide baseline

Using shares of customer preference, parcels are assigned to operators and the closest distribution centers.

SIRENE: Delivery centers

Scaling up: City-wide baseline

Using shares of customer preference, parcels are assigned to operators and the closest distribution centers.

SIRENE: Delivery centers

Scaling up: City-wide baseline

Using shares of customer preference, parcels are assigned to operators and the closest distribution centers.

SIRENE: Delivery centers

Methodology: Supply side

Vehicle routing and fleet composition problem

  • Minimize total cost of delivering all parcels for each center
    • Distance cost influenced by fuel / electricity cost
    • Fixed cost (per day) influenced by salaries and vehicle cost
       
  • Derive
    • Distances driven and related emissions
    • Fleet composition for each center

Novel approximation method

Visualisation platform

UCC platform

Timeline

  • Lectures
    • 10/01 8h30: Examples of large-scale models in transportation
    • 10/01 10h45: Modeling methods I
    • 13/01 14h00: Modeling methods II
    • 13/01 16h45: Introduction to the student project
       
  • Project work
    • 27/01 14h00 + 16h45: Intermediate results
    • 09/02 14h00 + 16h45: Exchange with other groups
    • 23/02 14h00 + 16h45: Final presentation

Transport planning: Overview

  • Goals
    • Cost-benefit analysis
    • Assessment of alternatives
    • Prediction

Sources: https://de.wikipedia.org/wiki/Westtangente_Z%C3%BCrich, openstreetmap.org

 

Transport planning: Overview

  • Goals
    • Cost-benefit analysis
    • Assessment of alternatives
    • Prediction
       
  • Use cases
    • Traditionally: Infrastructure
    • Today: Increasingly digital technology

Sources:
https://en.wikipedia.org/wiki/File:Highway_8_widening.png

https://commons.wikimedia.org/wiki/File:Self_driving_Uber_prototype_in_San_Francisco.jpg

Transport planning: Overview

  • Traditional approaches
    • High aggregation
    • Movements are flows
    • Locations are zones
    • Specific times of the day
       
  • Today's approaches
    • Individual entities
    • Movements are detailed in time and space
    • Whole daily analysis possible

Four-step models

Activity-based models

Four-step model: Overview

Generation

Distribution

Mode choice

Assignment

  • Four steps making use of different data sources
     
  • From static to more dynamic mobility decisions
     
  • Multiple possible feedback loops (most common example here)

Four-step model: Overview

Generation

Distribution

Mode choice

Assignment

  • Where do trips appear?
  • What is the destination of the trips?
  • What transport mode is used?
  • What congestion is caused?

Four-step model: Overview

Generation

Distribution

Mode choice

Assignment

Travel demand

Travel supply

  • Characterizes the need for mobility in the population for economic activity, leisure, ... 
  • Means that allow for mobility
  • Road infrastructure, rail network, ...

Four-step model: Overview

Generation

Distribution

Mode choice

Assignment

Travel demand

Travel supply

  • Characterizes the need for mobility in the population for economic activity, leisure, ... 
  • Means that allow for mobility
  • Road infrastructure, rail network, ...

Equilibrium

  • Given limited capacity,
    how is the system used?

Four-step model: Trip generation

  • Goal: Define statistically where trips starts, i.e. where they are "generated" or produced
     
  • Focus on peak hours in 4S, e.g. morning peak and focus on commuting activity
     
  • Either making use of direct data (e.g. from surveys) or based on population data, land use information, ...

Number of inabitants in Île-de-France

Four-step model: Trip generation

  • May be per homogeneous user group, e.g.
    • Single-person households
    • Multi-persons households
      without children
    • Multi-person households
      with children
    • Households with retired persons
       
  • Possible to use statistical models
O_{s,g} = f(X_s)

Generated trips

in zone s in group g

Trip generation model

Model inputs

Four-step model: Trip generation

  • Example: Linear model based on socioprofessional category (CS):
    • Employee
    • Worker
    • Retired
    • ...
       
  • Do we have reference number of trips for some of the zones? Then we can create a model from this formula! Example: Ordinary Least Squares (OLS)
f(X) = \sum_{CS} \lambda_{CS} \cdot x_{CS}

Model parameters (linear factors)

Census data (inhabitants)

\text{min}_\Lambda \sum_s (f(X_s|\Lambda) - \hat O_s)^2

Reference data

Four-step model: Trip distribution

  • Goal: Given the produced trips with their origin zone, define where they end = distribute the trips over a set of potential destination

Number of daily commutes arriving from 13th arrondissement

Four-step model: Trip distribution

  • Based on trip generation, we want to predict the number of trips going from zone s to zone t
     
  • Various ways to model flows between zones
    • Gravity model
    • Discrete choice model
    • Maximum entropy
       
  • Can be formulated per group g.
F_{s,t} = f(X_s, X_t)

Flow between s and t

Model

O1 ... ... On
D1
... Fst
...
Dn
O_s
D_t

Four-step model: Trip distribution

  • Growth factor approach
    • Useful if information on existing flows is available for many relations and we want to obtain an explicative model
       
  • Constrained approach
    • We have little flow information, but know about the total in each zone (e.g. population and workplaces)
F_{s,t} = \lambda_{s,t} \cdot O_t
\lambda_{s,t} = f(X_s, X_t)

Trip generation

Growth factor modeled through zone attributes

D_t = \sum_s F_{s,t}
O_s = \sum_t F_{s,t}
F_{s,t} = f(X_s, X_t)
Require
with

Four-step model: Trip distribution

  • Common approach: Gravity model
F_{s,t} = f(X_s, X_t) = \rho \cdot P_s \cdot A_t \cdot R_{s,t}
P_s = P(X_s)
A_t = A(X_t)

Production model, e.g. P = Population or Population Density

Attraction model, e.g. A = Workplaces or Workplace Density

R_{s,t} = A(X_s, X_t)

Resistance model, e.g. based on travel time or distance (also called impedance)

R_{s,t} = exp( -\beta \cdot \text{Distance}(s,t) )

Four-step model: Trip distribution

F_{s,t} = f(X_s, X_t) = \rho \cdot P_s \cdot A_t \cdot R_{s,t}
O_s = \sum_t F_{s,t}
O_s = \sum_t F_{s,t}
  • Common approach: Gravity model



     
  • If we know F, we can calibrate all models, e.g. using OLS ...
     
  • ... but we may better know required origins, i.e.

Four-step model: Trip distribution

F_{s,t} = f(X_s, X_t) = \rho \cdot P_s \cdot A_t \cdot R_{s,t}
O_s = \sum_t F_{s,t}
O_s = \sum_t F_{s,t} = \rho \cdot P_s \cdot \sum_t A_t \cdot R_{s,t}
  • Common approach: Gravity model



     
  • If we know F, we can calibrate all models, e.g. using OLS ...
     
  • ... but we may better know required origins, i.e.

Four-step model: Trip distribution

  • Common approach: Gravity model



     
  • If we know F, we can calibrate all models, e.g. using OLS ...
     
  • ... but we may better know required origins, i.e.


     
F_{s,t} = f(X_s, X_t) = \rho \cdot P_s \cdot A_t \cdot R_{s,t}
O_s = \sum_t F_{s,t}
O_s = \sum_t F_{s,t}
P_s = \frac{O_s}{\rho \sum_t A_t R_{s,t}}

Four-step model: Trip distribution

  • ... which can be inserted into the model ...



     
  • ... leading to



    with
     
  • If R is given or estimated independently (usually the case), the flows F are determined!
F_{s,t} = f(X_s, X_t) = \rho \cdot P_s \cdot A_t \cdot R_{s,t}
\alpha_s = \frac{1}{\sum_t A_t R_{s,t}}
F_{s,t} = f(X_s, X_t) = \alpha_s \cdot A_t \cdot R_{s,t} \cdot O_s
P_s = \frac{O_s}{\rho \sum_t A_t R_{s,t}}

Four-step model: Trip distribution

  • Including both origin and destination constraints gives



    with
F_{s,t} = f(X_s, X_t) = \alpha_s \cdot \beta_t \cdot O_s \cdot D_t \cdot R_{s,t}
P_s = \frac{O_s}{\rho \sum_t A_t R_{s,t}}
\alpha_s = \frac{1}{\sum_t A_t R_{s,t}}
\beta_t = \frac{1}{\sum_s P_s R_{s,t}}
A_t = \frac{D_t}{\rho \sum_s P_s R_{s,t}}
  • By construction, the origin and destination counts are replicated when iteratively solving

Timeline

  • Lectures
    • 10/01 8h30: Examples of large-scale models in transportation
    • 10/01 10h45: Modeling methods I
    • 13/01 14h00: Modeling methods II
    • 13/01 16h45: Introduction to the student project
       
  • Project work
    • 27/01 14h00 + 16h45: Intermediate results
    • 09/02 14h00 + 16h45: Exchange with other groups
    • 23/02 14h00 + 16h45: Final presentation

Four-step model: Mode choice

  • Goal: Given the infrastructure and the generated OD trips, which mode of transport should be used for them.
     
  • Expressed as mode share: How many percent of the trips on a OD relation are performed with mode m?
P[m]
m \in \{ car, pt, ... \}
\sum_m P[m] = 1
P[m] \geq 0

Utility maximization

  • Utility maximization is important concept in transport planning: Given a set of choices (modes, destinations, ...) we can assign a utility v to each alternative k.
     
  • We assume rational decision makers that always want to choose the alternative with the highest utility.
     
  • Homo oeconomicus
v_k = \beta^T X
k^* = \text{arg max}_k \{ v_1, ..., v_k, ... v_K \}

Utility maximization

  • Example: Choice between two public transport connections
v_k = \beta_\text{travelTime} \cdot x_{k, \text{travelTime}} + \beta_\text{interchanges} \cdot x_{k, \text{interchanges}}

Connection A

x_{A, \text{travelTime}} = 20\ \text{min}

Connection B

x_{B, \text{travelTime}} = 30\ \text{min}
x_{B, \text{interchanges}} = 0
x_{A, \text{interchanges}} = 1

Utility maximization

  • Example: Choice between two public transport connections
v_k = \beta_\text{travelTime} \cdot x_{k, \text{travelTime}} + \beta_\text{interchanges} \cdot x_{k, \text{interchanges}}

Connection A

x_{A, \text{travelTime}} = 20\ \text{min}

Connection B

x_{B, \text{travelTime}} = 30\ \text{min}
x_{B, \text{interchanges}} = 0
x_{A, \text{interchanges}} = 1

-0.6

-1.0

Utility maximization

  • Example: Choice between two public transport connections
v_k = \beta_\text{travelTime} \cdot x_{k, \text{travelTime}} + \beta_\text{interchanges} \cdot x_{k, \text{interchanges}}

Connection A

x_{A, \text{travelTime}} = 20\ \text{min}

Connection B

x_{B, \text{travelTime}} = 30\ \text{min}
x_{B, \text{interchanges}} = 0
x_{A, \text{interchanges}} = 1

-0.6

-1.0

-0.6 * 20 - 1.0 * 1 = -13

-0.6 * 30 - 1.0 * 0 = -19

Connection A is better alternative.

Utility maximization

  • Example: Mode choice model

Random Utility Models

  • How to estimate such models?
     
  • Assume K alternatives and N observed choices y described by index i.
     
  • We want to find the set of parameters such that all choices i are replicated correctly:
v_k(X_i) = \beta^T \cdot X_k
y_i \in \{ 1, ..., K \}
\beta
y_i = \text{arg max}_k \{ v_k(X_i|\beta) \} \ \ \forall i

Find               such that

Random Utility Models

  • Not easily possible: We cannot model reality sufficiently well, people have own tastes.
     
  • Hence, we introduce an error term.
     
  • This leads to a random utility maximization (RUM) model
u_{k,i} = v_{k,i} + \sigma \epsilon_{k,i}
E[\epsilon_{k,i}] = 0
\sigma \geq 0
k^*_i = \text{arg max}_k \{ u_{k,i} \}
k^*_i = \{ k \ | \ (u_{k,i} \geq u_{1,i}) \land \ (u_{k,i} \geq u_{2,i}) \land ... \}

Random Utility Models

  • McFadden has shown in the seventies that if error follows Extreme Value distribution ...
     
  • ... there is a closed form expression for the choice probability:

     
  • Two alternatives k:
    Binomial logit model
     
  • Multiple alternatives k:
    Multinomial logit model
u_k = v_k + \sigma \epsilon_k
\epsilon_{k,i} \sim \text{EV}
P[k] = \frac{\exp(\sigma^{-1} v_k)}{\sum_{k'}\exp(\sigma^{-1} v_{k'})}

Random Utility Models

  • Coming back to estimation:





     
  • Under multinomial logit assumption, we can write a (log-)likelihood function ...
     
  • ... which is proven convex and can be maximized using any optimization method!
P[k] = \frac{\exp(\sigma^{-1} v_k)}{\sum_{k'}\exp(\sigma^{-1} v_{k'})}
v_k(X_i) = \beta^T \cdot X_k
y_i \in \{ 1, ..., K \}
\mathcal{L}(\beta) = \prod_i P[y_i|X_i,\beta]
l(\beta) = \sum_i \log P[y_i|X_i,\beta]
\beta^* = \text{arg max}_{\beta} \sum_i \log P[y_i|X_i,\beta]

Random Utility Models

  • Multinomial logit is commonly used and part of larger class of discrete choice models.
     
  • Can also be used in distribution step.
  • Last step of 4S model

     
  • What are resulting flows on the roads?
     
  • What are the resulting travel times?

Four-step model: Assignment

  • Again, based on rational decision maker
     
  • Game theoretic perspective: Travellers compete about using the roads, each maximizing the utility they gain
     
  • Many ways of solving assignment problem

Four-step model: Assignment

  • Example: Two routes
    • Travellers on Route A:
    • Travellers on Route B:
    • Total travellers from S to E:
       
    • Travel time route A (normal road):
    • Travel time route B (highway):
       
    • Wardrop principle: Travellers tend to minimize their travel time.

Four-step model: Assignment

S

E

Route A

Route B

n_{A}
n_{B}
N = n_{A} + n_{B}
t_A(n_A) = 500 + n_A \cdot 2
t_B(n_B) = 1000 + n_B \cdot 1

How many people use each road? What are the travel times?

  • Example: Two routes
    • If travel time on A is shorter than B, people would switch to B, and vice versa. Hence, travel times, must be in equilibirum!

       
    • This gives

       

Four-step model: Assignment

S

E

Route A

Route B

n_{B}
N = n_{A} + n_{B}
t_A(n_A) = 500 + n_A \cdot 2
t_B(n_B) = 1000 + n_B \cdot 1
n_{A}
t_A(n_A) = t_B(n_B)
500 + 2 \cdot n_A = 1000 + 1 \cdot n_B
n_A = N - n_B

(*)

from (**)

(**)

  • Example: Two routes
    • If travel time on A is shorter than B, people would switch to B, and vice versa. Hence, travel times, must be in equilibirum!

       
    • This gives

       

Four-step model: Assignment

S

E

Route A

Route B

n_{B}
N = n_{A} + n_{B}
t_A(n_A) = 500 + n_A \cdot 2
t_B(n_B) = 1000 + n_B \cdot 1
n_{A}
t_A(n_A) = t_B(n_B)
500 + 2 \cdot n_A = 1000 + 1 \cdot n_B
n_A = N - n_B

(*)

from (**)

(**)

N = 1000

n_A = 433.33
n_B = 566.66
t_A = t_B = 1366.66
  • What about many different routes between two points?
     
  • What about many different start/end points in a network?
     
  • Wardrop defined general formulation, leading to a game-theoretic Nash equilibrium

Four-step model: Assignment

\text{min}_x \sum_a \int_0^{x_a} t_a(x_a) \text{d}x
\sum_k f_k^{rs} = q_{rs} \ \ \ \forall r, s
x_a = \sum_r \sum_s \sum_k \delta^{rs}_{k,a} f_k^{rs} \ \ \ \forall a
f_k^{rs} \geq 0
x_a \geq 0
s.t.

Four-step model: Feedback

Generation

Distribution

Mode choice

Assignment

  • Now travel times in the network are known. They can be fed back to the distribution stage (which travel times did we assume back then)?
     
  • 4S model can be run iteratively to bring stages in equilibrium.
     
  • Many caveats in terms of consistency and convergence (beyond the scope in this lecture).

Four-step model: Assignment

  • So far, Static Traffic Assignment (STA): Departure time of vehicles does not matter (we look at peak our time slice).
     
  • Methods for Dynamic Traffic Assignment (DTA) exist, which consider detailed movements of vehicles, traffic lights, ...

Activity-based models

  • Non-equilibrium models
    • Sequential decisions during simulation for each agent
    • Dynamic reaction to environment

Activity-based models

Activity 1

Activity 2

Activity 3

Decision

Decision

Analysis

Person 1

Activity 1

Activity 2

Person 1

Decision

  • Non-equilibrium models
    • Sequential decisions during simulation for each agent
    • Dynamic reaction to environment
       
  • Equilibrium models
    • Decision made for a whole day
    • All decisions of persons go into equilibrium after multiple iterations

Activity-based models

Activity 1

Activity 2

Activity 3

Person 1

Activity 1

Activity 2

Person 1

Analysis

Decision making

Iterations

  • Non-equilibrium models
    • Sequential decisions during simulation for each agent
    • Dynamic reaction to environment
       
  • Equilibrium models
    • Decision made for a whole day
    • All decisions of persons go into equilibrium after multiple iterations
       
  • Hybrid models

Activity-based models

  • Generally, detailed input data is needed to reach at detailed output
     
  • Data processing similar to 4S models, but much more complex and some components are dynamically treated in the simulation

Activity-based models

  • Population synthesis
    The task is to create a synthetic representation of the population with socio-demographical households and person attributes
     
  • Multitude of approaches
    • Iterative Proportional Fitting (IPF)
    • Iterative Proportional Updating (IPU)
    • Gibbs Sampling

Activity-based models

  • Population synthesis
    The task is to create a synthetic representation of the population with socio-demographical households and person attributes
     
  • Multitude of approaches
    • Iterative Proportional Fitting (IPF)
    • Iterative Proportional Updating (IPU)
    • Gibbs Sampling
    • Bayesian Networks

Activity-based models

Sun, L., Erath, A., 2015. A Bayesian network approach for population synthesis. Transportation Research Part C: Emerging Technologies 61, 49–62. https://doi.org/10.1016/j.trc.2015.10.010

  • Population synthesis
    The task is to create a synthetic representation of the population with socio-demographical households and person attributes
     
  • Multitude of approaches
    • Iterative Proportional Fitting (IPF)
    • Iterative Proportional Updating (IPU)
    • Gibbs Sampling
    • Bayesian Networks
    • Hidden Markov Models

Activity-based models

Saadi, I., Mustafa, A., Teller, J., Farooq, B., Cools, M., 2016. Hidden Markov Model-based population synthesis. Transportation Research Part B: Methodological 90, 1–21. https://doi.org/10.1016/j.trb.2016.04.007

  • Population synthesis
    The task is to create a synthetic representation of the population with socio-demographical households and person attributes
     
  • Multitude of approaches
    • Iterative Proportional Fitting (IPF)
    • Iterative Proportional Updating (IPU)
    • Gibbs Sampling
    • Bayesian Networks
    • Hidden Markov Models
    • Deep Generative Modeling
      Variational Auto Encoders

Activity-based models

Borysov, S.S., Rich, J., Pereira, F.C., 2019. How to generate micro-agents? A deep generative modeling approach to population synthesis. Transportation Research Part C: Emerging Technologies 106, 73–97. https://doi.org/10.1016/j.trc.2019.07.006

  • Synthesis of activity chains
    Given sociodemographic attributes, generate daily activity chains for the agents.
     
  • Today increasingly use of GPS / GSM trace data sets to train models
     
  • Some examples
    • Statistical Matching Approaches
    • Skeleton-based approaches
    • Sequential choice models (classic approach)
    • Sequential Alignment Methods (SAM)
    • Bayesian Networks
    • ...

Activity-based models

Joubert, J.W., de Waal, A., 2020. Activity-based travel demand generation using Bayesian networks. Transportation Research Part C: Emerging Technologies 120, 102804. https://doi.org/10.1016/j.trc.2020.102804

  • Further aspects:
    • Departure times from activities
    • Locations of activities
      • Potential Path Areas (PPA)
      • Space-time prisms
    • ...

Activity-based models

Yoon, S.Y., Deutsch, K., Chen, Y., Goulias, K.G., 2012. Feasibility of using time–space prism to represent available opportunities and choice sets for destination choice models in the context of dynamic urban environments. Transportation 39, 807–823. https://doi.org/10.1007/s11116-012-9407-8

  • As is demand generation, mobility simulation is often also more complex
     
  • Usually agent-based
     
  • Microscopic simulation
    • VISSIM, SUMO, ...
       
  • Mesoscopic simulation
    • MATSim, SimMobility,
      POLARIS, ...

Activity-based models

  • Convergence
    • Usually based on utility maximization principle
    • Detection of Nash equilibria
    • Output metric convergence
       
  • Calibration
    • Complex simulator (no closed form expression)
    • Noisy output (needs stochastic optimization)
    • Large run-times

Activity-based models: Challenges

Activity-based models: Examples

Timeline

  • Lectures
    • 10/01 8h30: Examples of large-scale models in transportation
    • 10/01 10h45: Modeling methods I
    • 13/01 14h00: Modeling methods II
    • 13/01 16h45: Introduction to the student project
       
  • Project work
    • 27/01 14h00 + 16h45: Intermediate results
    • 09/02 14h00 + 16h45: Exchange with other groups
    • 23/02 14h00 + 16h45: Final presentation

Grand Paris Express

  • One of largest infrastructure projects in Europe
     
  • Affecting mobility behaviour of large share of population in Île-de-France

Course project

  • Learn more about Grand Paris Express
     
  • Simple demand estimate for Grand Paris Express and its impact on existing public transport
     
  • Four groups:
    • Demand
    • Routing
    • GTFS
    • Mode choice

Please register for the groups:

Course project

Course: Grand Paris Express Project (2023)

By Sebastian Hörl

Course: Grand Paris Express Project (2023)

Université Gustave Eiffel

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