Impact of Low-Emission Zones on Spatial and Economic Inequalities using a Dynamic Transport Simulator

Lucas Javaudin

THEMA - Theoretical and Applied Economics Seminar

2023-04-04

Introduction

Context

  • Each year 430,000 Europeans die prematurely due to air pollution (European parliament)
  • Air pollution is mainly caused by nitrogen oxides (NOx) and particulate matter (PM) emitted by road vehicles
  • Popular instrument to improve air quality: Low Emission Zones (LEZ)

Low Emission Zones

  • In Europe, LEZs have been implemented in hundreds of cities
  • Starting in 2025, LEZs will be mandatory for French cities with more than 150,000 inhabitants
  • Benefits of LEZs: reducing local and global air pollution, congestion and noise pollution
Source: urbanaccessregulations.eu

Paris' Low Emission Zone

  • More than 5 million inhabintants are living in the LEZ
  • The LEZ represent around 10 % of the Île-de-France's road network
  • June 2021: Crit'air 4 vehicles and worse are banned (11 % of the fleet)
  • July 2023: Crit'air 3 vehicles and worse are banned (34 % of the fleet)

Crit'air Classes

Heterogeneous Effects

Not all individuals are affected in the same way by a Low Emission Zone.

Sources of heterogeneity:
  • Household living inside the LEZ vs outside the LEZ
  • High income vs low income
  • Owner of a clean car vs a polluting car
  • Car driver vs public-transit user

Metropolis: A Transport Simulator

We introduce a new transport simulator with the following characteristics:
  • agent-based (each individual is modeled as an autonomous entity)
  • based on economic theory (utility maximization)
  • multi-modal (it includes private and public transports)
  • dynamic (congestion is time-dependent and departure times are endogenous)
  • mesoscopic (vehicle flow are aggregated at link-level)
  • adapted to large-scale scenario (up to 1 million roads and 10 million agents)

Literature Review

Impact of Low Emission Zones:
  • Empirical evaluation: focus on environmental impact, ambiguous effect (Holman et al., 2015; Wolff, 2014; Margaryan, 2021)
  • Ex-ante evaluation:
    • Carslaw and Beevers (2022): approached based on traffic flow data, using an emission and dilution model
    • Dias et al. (2016): macroscopic transport model
    • Bok el al. (2022): agent-based model, focus on freight transport


Agent-based transport simulators:
  • MATSim (Axhausen et al., 2016): activity-based, behavior-oriented
  • SimMobility (Adnan et al., 2016): activity-based, hierarchical discrete choice modeling

Contributions

  • Development of a new agent-based transport simulator: Metropolis
  • Calibration to Paris' urban area (work in progress)
  • Evaluation of the Low Emission Zone of the Métropole du Grand Paris (work in progress)

Outline

  • Presentation of the transport simulator Metropolis
  • Application to Paris' urban area
  • Preliminary results: aggregate results, winners and losers from the LEZ

Metropolis

Objectives

  • Find a Nash equilibrium for a representative day in an urban area
  • Equilibrium: no agent can increase his / her utility by changing mode, departure time or route, given the expected traffic congestion
  • Compare baseline equilibrium with the equilibrium in other scenarios (e.g., new transit lines, Low Emission Zone, speed-limit change)
  • Results:
    • Aggregate impact of the policy on travel times, utilities, congestion, etc.
    • Spatial impact (e.g., city center vs suburbs)
    • Social impact (e.g., poor vs rich households)

Input of the Model

Road network

Vehicle types:
  • Headway between two vehicles
  • Passenger car equivalent
  • Speed function (representing speed limits)
  • Road restrictions

Input of the Model

Population

List of agents with the characteristics of their trips (for each mode available):
  • Origin and destination
  • Vehicle type
  • Travel-utility model (a function of the travel time; e.g., proportional to the value of time)
  • Schedule-utility model (a function of the departure and arrival time; e.g., alpha-beta-gamma model)

Basic Principle

  • Metropolis is an iterative model
  • At each iteration, four models are run successively (network skims computation, pre-day model, within-day model and day-to-day model)
  • The simulation stops when a convergence criteria is met or when the maximum number of iterations is reached

Network skims computation

  • Input: time-dependent travel-time function for each road of the road-network graph
  • Step 1: compute a time-dependent Hierarchy Overlay of the graph
  • Step 2: compute search spaces for each origin and destination node
  • Step 3: compute profile queries for each origin-destination pair
  • Output: time-dependent travel-time function for each origin-destination pair (with at least one trip)
Geisberger, R. and Sanders, P., 2010. Engineering time-dependent many-to-many shortest paths computation. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.

Pre-Day Model

  • Input: time-dependent travel-time function for each origin-destination pair
  • Output: mode, departure-time and route chosen by each agent
  • Backward induction process, based on trip utility

Bottleneck Equation

A trip generalized cost (minus utility) is \[ c(t_d, t_a) = \underbrace{\alpha \cdot (t_a - t_d)}_{\text{travel cost}} + \underbrace{\beta \cdot [t^* - t_a]_+ + \gamma \cdot [t_a - t^*]_+}_{\text{schedule-delay cost}} \]
  • \( t_d, t_a \): departure time, arrival time
  • \( \alpha \): value of time
  • \( t^* \): desired arrival time
  • \( \beta, \gamma \): penalty for early, late arrival
+
=

Pre-Day Model

Departure-Time Choice

A Continuous Logit Model combined with inverse transform sampling is used to simulate a departure time

Within-Day Model

  • Input: Chosen mode, departure time and route of each agent
  • Event-based model: Agents' actions are simulated in a chronological order
  • Output: Edges' travel-time functions
Time Event
03:00:03 Agent 91735 leaves origin through edge 317770
03:00:11 Agent 111697 leaves origin through edge 161026
03:00:27 Agent 111697 takes edge 161020

Congestion Modeling

  • Speed-density function
  • Traffic bottleneck
  • Queue propagation

Day-to-Day Model

  • Input: Expected and simulated edges' travel-time functions
  • Learning process based on Markov decision processes
  • Output: Expected edges' travel-time functions for next iteration
\[ {tt}^e_{\tau + 1} = \lambda \cdot {tt}^e_{\tau} + (1 - \lambda) \cdot {tt}^s_{\tau} \]

Convergence

Ways to check convergence to a Nash equilibrium:
  • Choices do not change
  • Expected congestion does not change
  • Expected congestion matches simulated congestion




  • No proof on stability and uniqueness of equilibrium

Example Applications

  • Air pollution (Le Frioux, de Palma, Blond)
  • Ride-sharing (de Palma, Delle Site, Ghoslya, Javaudin)
  • Public transit and Grand-Paris Express evaluation (Javaudin)
  • Automatic calibration for any French cities with various open datasets
Transport simulator -> Emissions -> Dispersion -> Population exposure -> Monetarization

Application

Introduction

  • Scope: Île-de-France, trips by car between 3AM and 10AM, all purposes, representative working day
  • Limits:
    • No mode choice
    • No car-ownership model
    • Time restrictions are not taken into account
    • Cheating and exceptions are not considered

Input: Road network

  • Source: OpenStreetMap
  • Highway types: motorway, trunk, primary, secondary, tertiary, living street, unclassified and residential
  • Living streets, unclassified and residential roads are discarded when not used
  • Final network has 40 852 km of roads (out of 91 859 km in the full network)

Input: Road network

Input: Population

  • Generation of a synthetic population using Hörl and Balac (2021)
  • Data sources: INSEE census, household travel survey, FiLoSoFi (household income), BD-TOPO (buildings data), SIRENE (entreprise census) and BPE (service and facility census)
  • Simulated household-level characteristics: car availability, bike availability, income
  • Simulated individual-level characteristics:
    • all activities performed during a day (home, work, education, leisure, shopping, other) with the activity duration and exact location
    • age, employment status, sex, socio-professional category, driving license, public-transit subscription
  • Final population: 193 235 agents, with 254 585 trips (simulation is scaled down to 10 %)
Hörl, S. and Balac, M., 2021. Synthetic population and travel demand for Paris and Île-de-France based on open and publicly available data. Transportation Research Part C: Emerging Technologies, 130, p.103291.

Input: Population

Example agent

Household
  • Members: 2
  • Car available: 1
  • Bike available: 2
  • Disposable income: 13 101 euros (monthly)
Individual
  • Age: 60
  • Employed: Yes
  • Sex: Woman
  • Socio-professional class: 3 (Cadres et professions intellectuelles supérieures)
  • Driving license: Yes
  • Public-transit subscription: No

Input: Population

Example agent

Activities
  • Home until 07:33
  • Work from 09:03 to 12:43
  • Leisure from 12:48 to 13:28
  • Work from 13:33 to 20:03
  • Home from 20:38 to 21:03
  • Leisure from 23:23 to 23:33

Input: Population

Vehicle Types

  • Data: Statistics on the vehicle fleet from the French Ministry of Transport (2021)
  • INSEE Communes level
  • A vehicle is randomly drawn for each agent based on the vehicle fleet from his / her home city

Scenarios

  • No-LEZ simulation: Simulation without the Low Emission Zone
  • LEZ-2021 simulation: Crit'air 4 and 5 are forbidden (6.2 % of agents)
  • LEZ-2023 simulation: Crit'air 3, 4 and 5 are forbidden (19.1 % of agents)


Note: All vehicles are allowed in the LEZ if the trip starts or ends inside the LEZ (47.1 % of the trips in the LEZ-2023 scenario)

A Note on Calibration

  • Values to estimate or calibrate: road capacities, agents' preferences (value of time, schedule-delay penalties), activities' desired arrival times
  • Three options:
    1. Use a value from the literature
    2. Estimate a value from revealed or declared preferences (e.g., from a travel survey data)
    3. Calibrate the value to match observed data (e.g., traffic counts, distribution of arrival times)
  • In this work: road capacities and preferences are taken from the literature; desired arrival times are set to observed arrival times

Calibration

Travel time penalties at intersections are calibrated to match travel time distribution

Calibration

Distribution of desired arrival times is calibrated to match arrival time distribution

Results

Running Time

  • Number of iterations: 750
  • Total running time: 60 hours 15 minutes
  • Running time per iteration: 4'49''

Convergence

Choice stability

  • Average departure-time shift (in absolute value) is 1.53 seconds (maximum is 154 seconds), at last iteration
  • On average, the route used by each agent is the same as the one from the previous iteration for 97.79 % of its length, at last iteration

Convergence

Expected congestion stability

The average travel time anticipated is equal to 16 minutes and 58 seconds (\(\pm\)1s) for the last 50 iterations.

Convergence

Correctness of Anticipations

  • EXPECT: relative difference between the anticipated and simulated travel times
  • On average, agents under-estimate or over-estimate their travel time by 9.5 % (= 1'45''), at the last iteration

Aggregate Results

No LEZ LEZ-2021 LEZ-2023
Departure time 07:35:16 07:35:15 07:35:20
Travel time 17'42'' 17'45'' 17'56''
Route length (m) 13 617 13 616 13 629
Generalized cost (euros) 9.56 9.61 9.77


Global impact (for 1.9 M car drivers each day between 3AM and 10AM):
  • 8.696 million euros in the LEZ-2021 scenario compared to No-LEZ
  • 39.420 million euros in the LEZ-2023 scenario compared to No-LEZ

Results by Population Groups

Comparison between LEZ-2023 and No-LEZ scenario, by groups
Share \( \Delta \) travel time \( \Delta \) route length (m) \( \Delta \) cost (euro)
Full in 27.0 % +4'' +6 +0.09
Start or end in LEZ 21.2 % +27'' +3 +0.27
Cross / Allowed 0.7 % +1'6'' -45 +0.47
Do not cross / Allowed 32.4 % +5'' 0 +0.03
Cross / Banned 0.4 % +4'23'' +3067 +1.37
Do not cross / Banned 18.3 % +5'' -3 +0.04

Traffic Counts Change

Traffic Counts Change

Basic Cost-Benefit Analysis

What if the owner of polluting cars had to switch to public-transit when the trip is unfeasible?

  • Number of car drivers decrease from 193 235 to 162 065 (-31 170; 16 % decrease)
  • Average travel time decreases from 16'20'' to 13'28'' (18 % decrease)
  • Average route length decreases from 13 009 m to 12 922 m (1 % decrease)
  • Average generalized cost decreases by 0.98 euros


Total generalized cost decreases if the average cost of switching to public-transit is smaller than \( \mathbf{0.98 * \frac{162065}{31170} = 5.10} \) euros

Conclusion

Conclusion

Results
  • Metropolis is adapted to study the heterogeneous effect of a policy (such as a LEZ)
  • When considering only traffic congestion, Paris' LEZ has
    • no significant effect on the people that do not need to cross the LEZ
    • an ambiguous effect on the people owning a clean car that need to cross the LEZ
    • a negative effect on the people owning a polluting car that need to cross the LEZ


Future works
  • Mode choice
  • Car ownership
  • Calibration and validation
  • Improve convergence
  • Additional results (results by demographic groups, air pollution)

Thank you