# Incentive Design for Eco-driving in Urban Transportation Networks

M. Umar B. Niazi  Jung-Hoon Cho  Munther A. Dahleh  Roy Dong  Cathy Wu M. U.
B. Niazi and M. A. Dahleh are with the Laboratory for Information and Decision
Systems, Department of Electrical Engineering and Computer Science,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA. Email:
<EMAIL_ADDRESS><EMAIL_ADDRESS>Cho and C. Wu are with the Laboratory for
Information and Decision Systems, Department of Civil and Environmental
Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Email<EMAIL_ADDRESS><EMAIL_ADDRESS>Dong is with the Department of
Industrial and Enterprise Systems Engineering, University of Illinois at
Urbana-Champaign, Urbana, IL 61801, USA. Email<EMAIL_ADDRESS>work
was partially supported by the National Science Foundation (NSF) under grant
number 2149548, the European Union’s Horizon Research and Innovation Programme
under Marie Skłodowska-Curie grant agreement No. 101062523, and the Kwanjeong
scholarship.

###### Abstract

Eco-driving emerges as a cost-effective and efficient strategy to mitigate
greenhouse gas emissions in urban transportation networks. Acknowledging the
persuasive influence of incentives in shaping driver behavior, this paper
presents the ‘eco-planner,’ a digital platform devised to promote eco-driving
practices in urban transportation. At the outset of their trips, users provide
the platform with their trip details and travel time preferences, enabling the
eco-planner to formulate personalized eco-driving recommendations and
corresponding incentives, while adhering to its budgetary constraints. Upon
trip completion, incentives are transferred to users who comply with the
recommendations and effectively reduce their emissions. By comparing our
proposed incentive mechanism with a baseline scheme that offers uniform
incentives to all users, we demonstrate that our approach achieves superior
emission reductions and increased user compliance with a smaller budget.

##  I Introduction

In many countries, transportation accounts for a significant share of
greenhouse gas emissions, ranging from a quarter to one-third of the total
emissions. Numerous strategies are being employed to improve fuel efficiency
and decrease emissions in on-road vehicles. These approaches encompass
advancements in engine and vehicle technologies as well as improvements in
fuel quality. However, eco-driving stands out as the most cost-effective and
highly efficient means of reducing emissions from road transportation [1].
Research has consistently demonstrated that eco-driving practices can yield
substantial reductions in vehicle emissions, ranging from 10% to as high as
45% [2]. These findings underscore the immediate and significant role that
eco-driving can play in addressing the challenge of climate change.

Eco-driving is a set of techniques that aim to improve fuel efficiency and
reduce emissions by optimizing vehicle operation and driver behavior. Some of
the techniques include:

  * •

Selecting less congested routes: This reduces fuel consumption and emissions
by minimizing idling and stop-and-go traffic.

  * •

Improving driving style: This includes avoiding aggressive acceleration and
braking, and maintaining a steady speed. These techniques reduce fuel
consumption and emissions by minimizing energy losses due to inefficient
vehicle operation.

It is important to note that opting for less congested routes may result in
longer travel times, and improving driving style might require adjustments
that some drivers find inconvenient. To overcome these challenges and promote
eco-driving, there may be a need for transportation system operators to
introduce incentives that encourage individuals to adopt these practices for
the purpose of emission reduction.

A considerable amount of evidence supports the effectiveness of incentive
programs in promoting eco-driving. For instance, [3] observed a reduction of
over 10% in fuel consumption and emissions after monetary incentives were
introduced to bus drivers. Remarkably, they found that the cost savings in
fuel for bus companies exceeded the incentives provided to drivers. Comparable
results were obtained by [4] and [5] when incentivizing heavy-duty vehicle
drivers in logistic companies. Furthermore, behavioral studies, such as [6]
and [7], demonstrate that monetary incentives are more effective in changing
driver behavior than providing informational content on eco-driving through
in-vehicle human-machine interfaces. Nevertheless, the incentive schemes
presented in this body of literature are overly simplistic and do not cater to
various driver types with differing preferences.

In this paper, we propose a digital platform that incentivizes human drivers
to eco-drive with the goal of reducing the overall emissions of an urban
transportation network. At the beginning of their trips, the users provide
private information and preferences to the platform, such as their origin and
destination, vehicle type, and preferred travel time vs. emissions trade-offs.
Using this information, the platform computes feasible eco-routing and eco-
driving strategies for each user. Then, it devises personalized incentives and
eco-driving recommendations to users by minimizing overall emissions subject
to budget constraints.

The overarching goal of the platform is to minimize the network’s emissions
while optimally allocating a limited budget as incentives to drivers. Our
approach is unique in its integration of a traffic simulator into the
incentive mechanism. The simulator predicts traffic conditions and calculates
corresponding eco-driving recommendations and optimal incentives that can
potentially reduce emissions by a certain amount. This feature allows us to
account for real-time traffic variations in our incentive strategy.

The paper is organized as follows. Section II introduces the incentive
mechanism for eco-driving. Section III delves into some technical observations
and remarks. Section IV presents numerical experiments. Finally, Section V
summarizes the findings and highlights potential future directions.

##  II Incentive Mechanism for Eco-driving

###  II-A Model Setup and Assumptions

UsersEco-planner Provide information about their trips and their preferences
Proposes optimal eco-driving recommendations and incentives to the users
Complete their trips by either complying or not complying with the eco-driving
recommendations Transfers incentives to the users who complied with the eco-
driving recommendations Figure 1: Steps in the proposed incentive mechanism
(from left to right).

We consider an urban transportation network denoted by a graph
$\mathcal{N}=(\mathcal{I},\mathcal{L})$, where $\mathcal{I}$ denotes the set
of intersections and $\mathcal{L}\subseteq\mathcal{I}\times\mathcal{I}$
denotes the set of links/roads. We aim to design an eco-planner digital
platform $\mathsf{P}$ that plans and recommends eco-driving strategies to its
users in the network $\mathcal{N}$ before they embark on their trips. The eco-
planner $\mathsf{P}$ also commits to providing certain incentives if the users
comply with the eco-driving recommendations to reduce their emissions at the
expense of increased travel time. The users who subscribe to $\mathsf{P}$ are
denoted by a set $U=\\{1,\dots,n\\}$, where $n$ denotes the number of users.

Before starting her commute, each user $i$, $i\in U$, asks $\mathsf{P}$ to
plan the journey by providing her private information, which includes the
following:

  * •

Origin-Destination pair $(o_{i},d_{i})\in\mathcal{L}\times\mathcal{L}$, which
corresponds to the start and end points of $i$’s journey

  * •

Vehicle type $v_{i}\in V$, where $V=\\{v_{1},\dots,v_{l}\\}$ is the set of
finite number of vehicle types

  * •

Emissions vs. travel time trade-off parameter $\vartheta_{i}\in[0,1]$.

For instance, vehicle type may correspond to not only its classification
(sedan, SUV, etc.) but also its engine and fuel types. This information is
needed so that $\mathsf{P}$ can predict the emissions of user $i$ on her
commute between $(o_{i},d_{i})$ on different routes with different traffic
conditions. Emissions vs. travel time trade-off parameter $\vartheta_{i}$ is
needed to assess the urgency of user $i$ for her trip, and whether she will
accept a certain amount of incentive to reduce her emissions by eco-driving by
compromising slightly on her travel time.

After obtaining the private information
$(o_{i},d_{i},v_{i},\vartheta_{i})_{i\in U}$, the eco-planner $\mathsf{P}$
predicts the best eco-driving strategies in terms of a route choice and
driving style for each user depending on the predicted traffic conditions for
their trips. Then, $\mathsf{P}$ recommends those strategies and persuades the
users to follow those strategies by offering incentives
$\gamma_{1},\dots,\gamma_{n}$ subject to $\mathsf{P}$’s budget constraint
$\sum_{i=1}^{n}\gamma_{i}\leq B$, where $B\in\mathbb{R}_{>0}$ is the total
budget of $\mathsf{P}$. The users complete their trips by either complying or
not complying with the eco-driving recommendations, and their commutes result
in a certain outcome in terms of their individual emissions. Finally,
$\mathsf{P}$ transfers the incentives to the users based on their compliance
with the recommendations and to compensate for their increased travel times
due to their eco-driving and reducing emissions. The incentive mechanism is
summarized by an illustration in Fig. 1.

In the current paper, we assume that users provide true information to the
eco-planner and do not strategically manipulate it to maximize their rewards,
which avoids the issue of adverse selection. Incorporating incentive
compatibility constraints will be a topic of our future work. Secondly, to
address the issue of moral hazard, whereby the behavior and outcomes of users
are not observable, we assume $\mathsf{P}$ employs vehicle telematics [8, 9]
to measure the driving style and emissions of each user during her commute.
Finally, we assume traffic conditions and network structures where eco-driving
results in lower emissions and longer travel times. For example, choosing a
longer route with fewer intersections would yield lower emissions as compared
to choosing a shorter route through an urban area with plenty of intersections
and stop signs. The former route may result in longer travel times, but
because of smooth driving, it would result in lower emissions than the latter
route. It is important to remark that there could be other scenarios, e.g.,
eco-driving near signalized intersections [10], where eco-driving improves
both travel times and emissions. However, in these scenarios, user’s and eco-
planner’s objectives are aligned, and the issue becomes one of information
design rather than incentive design.

###  II-B Users’ Objectives

Since eco-driving strategies can increase travel time by requiring drivers to
take longer routes or drive at slower speeds, we assume that drivers, being
cost minimizers, optimize their driving behaviors based on the utilities they
place on reducing their emissions/fuel consumption versus reducing their
travel times. Let
$x_{i}=[\begin{array}[]{cc}x_{i}^{t}&x_{i}^{e}\end{array}]^{\top}\in
X_{i}\subset\mathbb{R}_{>0}^{2}$ denote the outcome of user $i$’s commute
between the origin $o_{i}$ and the destination $d_{i}$, where $x_{i}^{e}$
denotes her emissions and $x_{i}^{t}$ denotes her travel time. Here, $X_{i}$
is assumed to be a convex set denoting all feasible emission-travel time pairs
achievable via different driving styles and route choices for $(o_{i},d_{i})$
given $i$’s vehicle type $v_{i}$ and traffic conditions in the network
$\mathcal{N}$. In other words, each point $x_{i}\in X_{i}$ denotes an
emissions-travel time outcome corresponding to a certain route and driving
style.

Each user $i$ chooses her route and driving style that minimizes her cost
function

$c_{i}(x_{i})=(1-\vartheta_{i})x_{i}^{t}+\vartheta_{i}x_{i}^{e}$

where $\vartheta_{i}\in[0,1]$ is user $i$’s emissions vs. travel time trade-
off parameter. In other words, $i$ solves the following convex optimization
problem:

$\text{minimize}~{}c_{i}(x_{i})\triangleq\theta_{i}^{\top}x_{i}~{}\text{subject
to}~{}x_{i}\in X_{i}$ (1)

where
$\theta_{i}=[\begin{array}[]{cc}1-\vartheta_{i}&\vartheta_{i}\end{array}]^{\top}$
is $i$’s preference parameter. Let

$x_{i}^{\text{nom}}=\operatorname*{arg\,min}_{x_{i}\in X_{i}}c_{i}(x_{i})$ (2)

be the nominal outcome of user $i$.

###  II-C Computation of Feasible Sets

Let $R_{i}$ denote the set of routes for the origin-destination pair
$(o_{i},d_{i})$, where $r_{i,j}\in R_{i}$ is the $j$-th route containing a
path in $\mathcal{N}$ starting from $o_{i}$ and ending at $d_{i}$. The eco-
planner invokes a traffic simulator $\mathsf{S}$ to compute the feasible sets
of each user. In other words, the simulator $\mathsf{S}$ takes the network
$\mathcal{N}$, origin-destination pair $(o_{i},d_{i})$, and vehicle type
$v_{i}$ as inputs, and outputs the feasible set
$X_{i}\subset\mathbb{R}_{>0}^{2}$.

The first step of the simulator involves computation of $p$ shortest routes
$R_{i}=(r_{i,1},\dots,r_{i,p})$ in $\mathcal{N}$ between $(o_{i},d_{i})$.
After that, for every $j\in[p]$, $\mathsf{S}$ computes a set of
$m\in\mathbb{N}$ points $\hat{X}_{ij}=\\{x_{i,j}^{1},\dots,x_{i,j}^{m}\\}$,
which results from simulating different eco-driving as well as normal driving
styles on route $r_{i,j}$ under different traffic conditions. Finally,
$\mathsf{S}$ outputs

$X_{i}=\mathrm{conv}(\hat{X}_{i1},\dots,\hat{X}_{ip})$ (3)

where $\mathrm{conv}(\cdot)$ denotes the convex hull. Notice that computing
feasible sets as in (3) renders (1) to be a linear program.

###  II-D Incentive Mechanisms

Before starting their trips, users interact with the eco-planner by providing
their information (see Fig. 1). The eco-planner then proposes incentives
$\gamma_{1},\dots,\gamma_{n}$ to the users conditioned on their following
corresponding eco-driving strategies to reduce emissions. Here,
$\gamma_{i}\in\mathbb{R}_{\geq 0}$ denotes the incentive user $i$ receives
from the eco-planner $\mathsf{P}$ at the end of her trip between
$(o_{i},d_{i})$ if she followed the recommended route and eco-driving
strategies to achieve the recommended outcome $x_{i}^{\text{rec}}\in X_{i}$.

####  II-D1 Baseline Incentive Mechanism

In this paper, we consider the baseline incentive mechanism as equally
allocating the total budget among all users of the same type, where we do not
consider their parameters $\vartheta_{i}$’s. For instance, if all the users
have the same origin-destination pairs $(o_{i},d_{i})$ and the same vehicle
types $v_{i}$, then each user $i$ is offered the same incentive
$\gamma_{i}^{\text{BL}}=B/n$ conditioned on achieving the recommended outcome
$x_{i}^{\text{rec}}$. In this paper, we use this baseline mechanism to compare
with our proposed optimal mechanism. In our future work, other baselines will
also be devised for comparison.

####  II-D2 Optimal Incentive Mechanism

To compute the optimal eco-driving recommendations and corresponding
incentives for each user while adhering to budget constraints, the proposed
incentive mechanism (Fig. 1) involves the following steps:

  1. 1.

Users report their information
$(o_{i},d_{i},v_{i},\vartheta_{i})_{i=1,\dots,n}$ to the eco-planner
$\mathsf{P}$.

  2. 2.

$\mathsf{P}$ invokes the simulator $\mathsf{S}$ and obtains

$X_{i}=\mathsf{S}(\mathcal{N},o_{i},d_{i},v_{i}),\;\forall i\in[n].$

  3. 3.

Using $X_{i}$, $\mathsf{P}$ solves (1) and finds $x_{i}^{\text{nom}}$ from
(2).

  4. 4.

$\mathsf{P}$ solves the following linear program:

minimize $\displaystyle\xi^{\top}x^{\text{rec}}$ (4a) subject to
$\displaystyle c_{i}(x_{i}^{\text{rec}})-\gamma_{i}\leq
c_{i}(x_{i}^{\text{nom}})$ (4b) $\displaystyle\sum_{i=1}^{n}\gamma_{i}\leq
B,\gamma_{i}\geq 0$ (4c) $\displaystyle x_{i}^{\text{rec}}\in X_{i},~{}\forall
i\in[n]$ (4d)

where
$x^{\text{rec}}=[\begin{array}[]{ccc}x_{1}^{\text{rec}}&\dots&x_{n}^{\text{rec}}\end{array}]\in
X_{1}\times\dots\times X_{n}\subset\mathbb{R}_{>0}^{2n}$ is a vector of
outcomes recommended by $\mathsf{P}$, $B$ is the total budget of $\mathsf{P}$,
and

$\xi^{\top}=1_{n}^{\top}\otimes[\begin{array}[]{cc}0&1\end{array}]=[\begin{array}[]{ccccc}0&1&\dots&0&1\end{array}]$

is a vector indicating that the goal of $\mathsf{P}$ is to minimize the total
emissions of all users subject to the budget constraint (4c).

  5. 5.

$\mathsf{P}$ proposes incentives $\gamma_{1},\dots,\gamma_{n}$ to the users
conditioned on complying with the recommended routes and eco-driving
strategies that yield the emission-travel time outcomes
$x_{1}^{\text{rec}},\dots,x_{n}^{\text{rec}}$, respectively.

Notice that the linear program (4) can be written in the standard form by
choosing

$\gamma_{i}=\theta_{i}^{\top}(x_{i}^{\text{rec}}-x_{i}^{\text{nom}})$ (5)

and rewriting the convex polytope $X_{i}$ in (3) as

$X_{i}=\\{x_{i}\in\mathbb{R}_{>0}^{2}:A_{i}x_{i}\leq b_{i}\\}$ (6)

where $A_{i}\in\mathbb{R}^{k\times 2}$ and $b_{i}\in\mathbb{R}^{k}$ with
$k\leq mp$. Here, $p$ corresponds to the number of routes chosen between the
origin $o_{i}$ and the destination $d_{i}$, and $m$ is the number of different
driving styles simulated on every route by $\mathsf{S}$. Thus, we can
equivalently write (4) as

minimize $\displaystyle\xi^{\top}x^{\text{rec}}$ (7a) subject to
$\displaystyle\mathcal{A}x^{\text{rec}}\leq\beta$ (7b)

where

$\mathcal{A}=\left[\begin{array}[]{ccc}\theta_{1}&\dots&\theta_{n}\\\
A_{1}&&\\\ &\ddots&\\\
&&A_{n}\end{array}\right],\quad\beta=\left[\begin{array}[]{c}B+\theta^{\top}x^{\text{nom}}\\\
b_{1}\\\ \vdots\\\ b_{n}\end{array}\right]$

with
$\theta^{\top}=[\begin{array}[]{ccc}\theta_{1}&\dots&\theta_{n}\end{array}]$
and
$x^{\text{nom}}=[\begin{array}[]{ccc}x_{1}^{\text{nom}}&\dots&x_{n}^{\text{nom}}\end{array}]^{\top}$.

##  III Technical Observations and Remarks

###  III-A Computed Feasible Sets are only Approximations

We remark that the feasible sets obtained from the simulator are only
approximations of the true feasible sets of the users. However, using
approximated feasible sets does not significantly impact the incentive
mechanism. Moreover, the approximation can be refined by simulating many
number $m$ of traffic scenarios and driving styles. Therefore, depending on
the quality of the approximation, the eco-planner $\mathsf{P}$ can relax the
terms of the contract by transferring the incentive to user $i$ if her actual
outcome $x_{i}$ at the end of the trip turned out to be inside a ball of
certain radius around the recommended outcome $x_{i}^{\text{rec}}$.

To elucidate, the eco-planner $\mathsf{P}$ computes an approximated feasible
set $\hat{X}_{i}\subseteq X_{i}$ from the simulator $\mathsf{S}$,
$\hat{X}_{i}$ is a convex polytope. The inclusion of $\hat{X}_{i}$ inside
$X_{i}$ is because $X_{i}$ is convex and no simulated point can be outside of
$X_{i}$. In the case where $\mathsf{S}$ is able to simulate the boundary
points of $X_{i}$, $\hat{X}_{i}$ will be a convex polytope inscribed inside
$X_{i}$. Nevertheless, the eco-planner $\mathsf{P}$ will compute the nominal
solution $\hat{x}_{i}^{\text{nom}}\in\hat{X}_{i}$ to (2), which will be a
projection of the true $x_{i}^{\text{nom}}\in X_{i}$ onto $\hat{X}_{i}$.
Putting computational issues aside, if the simulator $\mathsf{S}$ simulates a
very large number of cases $m$, the approximation $\hat{X}_{i}$ can be
arbitrarily improved. Keeping this in mind, $\mathsf{P}$ transfers the
incentive if the actual outcome $x_{i}\in X_{i}$ is with an
$\varepsilon$-Euclidean distance from the recommended outcome
$x_{i}^{\text{rec}}\in\hat{X}_{i}$.

###  III-B Users Nominal Outcomes are on the Pareto Fronts of their Feasible
Sets

It is important to note that the nominal solution $x_{i}^{\text{nom}}$ of user
$i$ lies at a certain part of the boundary of her feasible set $X_{i}$. To
explain this fact, we define the following notions. We say
$x_{i}=[\begin{array}[]{cc}x_{i}^{t}&x_{i}^{e}\end{array}]^{\top}\in X_{i}$
pareto dominates
$\tilde{x}_{i}=[\begin{array}[]{cc}\tilde{x}_{i}^{t}&\tilde{x}_{i}^{e}\end{array}]^{\top}\in
X_{i}$ if either of the following two conditions hold:

  1. (i)

$x_{i}^{t}\leq\tilde{x}_{i}^{t}$ and $x_{i}^{e}<\tilde{x}_{i}^{e}$

  2. (ii)

$x_{i}^{t}<\tilde{x}_{i}^{t}$ and $x_{i}^{e}\leq\tilde{x}_{i}^{e}$.

Moreover, $x_{i}$ is said to be pareto optimal if there does not exist
$\tilde{x}_{i}\in X_{i}$ that pareto dominates $x_{i}$. Then, the pareto front
of the feasible $X_{i}$ is defined as

$\text{PF}(X_{i})=\\{x_{i}\in X_{i}:x_{i}~{}\text{is pareto optimal}\\}$

which will be a subset of $X_{i}$’s boundary. Then, the following fact can be
stated.

######  Fact 1.

Let $x_{i}^{\text{nom}}$ be the solution of the convex problem (2), then
$x_{i}^{\text{nom}}\in\text{PF}(X_{i})$.

###### Proof.

Assume $x_{i}^{\text{nom}}\notin\text{PF}(X_{i})$. Then, $x_{i}^{\text{nom}}$
is not pareto optimal and there exists $v\in\mathbb{R}_{\geq 0}^{2}$, $v\neq
0_{2\times 1}$, such that $x_{i}^{\text{nom}}-v$ pareto dominates
$x_{i}^{\text{nom}}$ and

$c_{i}(x_{i}^{\text{nom}})=\theta_{i}^{\top}x_{i}^{\text{nom}}>\theta_{i}^{\top}(x_{i}^{\text{nom}}-v)=c_{i}(x_{i}^{\text{nom}}-v)$

which is a contradiction becausue $x_{i}^{\text{nom}}$ being the solution of
(2) is the minimizer of $c_{i}(\cdot)$. ∎

###  III-C Users Reporting their Preferred Travel Times instead of their
Trade-off Parameters

Some might argue that reporting the emissions vs. travel time trade-off
parameter, $\vartheta_{i}$, can be challenging for users in reality. Aside
from its vague and technical interpretation, it is possible that users may not
know the exact value of their parameters, let alone report them truthfully.
Instead, the eco-planner may ask the user to report their preferred (i.e.,
nominal) travel time $x_{i}^{t,\text{nom}}\in X_{i}$ between $o_{i}$ and
$d_{i}$. Since we know from Fact 1 that
$x_{i}^{\text{nom}}\in\text{PF}(X_{i})$, we can find the corresponding
emissions $x_{i}^{e,\text{nom}}$ that $i$ would incur for their nominal route
selection and driving style. Then, the question is how to estimate
$\theta_{i}=[\begin{array}[]{cc}\vartheta_{i}&1-\vartheta_{i}\end{array}]^{\top}$
given that $x_{i}^{\text{nom}}$ is the minimizer of the cost function
$c(x_{i};\theta_{i})$ in (1)?

A simple algorithm to estimate $\theta_{i}$ is as follows. Sample
$\vartheta_{i}\in[0,1]$ and obtain
$0=\vartheta_{i}^{1}<\vartheta_{i}^{2}<\dots<\vartheta_{i}^{s}=1$ for some
sufficiently large $s\in\mathbb{N}$. For every $\vartheta_{i}^{j}$, solve (2)
and obtain the solution $x_{i}^{\text{PF}_{j}}\in\text{PF}(X_{i})$. Then,

$s^{*}=\operatorname*{arg\,min}_{j\in\\{1,\dots,s\\}}\|x_{i}^{\text{nom}}-x_{i}^{\text{PF}_{j}}\|$

and

$\hat{\theta}_{i}=\left[\begin{array}[]{c}\vartheta_{i}^{s^{*}}\\\
1-\vartheta_{i}^{s^{*}}\end{array}\right].$ (8)

One can refine this solution arbitrarily by subsequently sampling again around
$x_{i}^{\text{PF}_{s^{*}}}$, where the idea is to coarsely sample initially
and then keep on refining the samples around the closest solutions in the next
iteration.

When users their preferred travel times instead of their emissions vs. travel
time trade-off parameters, the steps involved in the incentive mechanism can
be modified as follows:

  1. 1.

Users report their preferred travel time, vehicle types and origin-destination
pairs $(x_{i}^{t,\text{nom}},v_{i},o_{i},d_{i})_{i=1,\dots,n}$ to the eco-
planner $\mathsf{P}$.

  2. 2.

$\mathsf{P}$ invokes the simulator $S$ and obtains

$\hat{X}_{i}=S(\mathcal{N},v_{i},o_{i},d_{i}),\;\forall i\in[n]$

where
$\hat{X}_{i}=\\{x_{i}\in\mathbb{R}_{>0}^{2}:\hat{A}_{i}x_{i}\leq\hat{b}_{i}\\}$
is a convex polytope.

  3. 3.

Using $x_{i}^{t,\text{nom}}$, $\mathsf{P}$ estimates $x_{i}^{e,\text{nom}}$
using Fact 1 and $\hat{\theta}_{i}$ using (8).

  4. 4.

$\mathsf{P}$ solves the following linear program:

minimize $\displaystyle\xi^{\top}x^{\text{rec}}$ (9a) subject to
$\displaystyle\hat{\mathcal{A}}x^{\text{rec}}\leq\hat{\beta}$ (9b)

where

$\hat{\mathcal{A}}=\left[\begin{array}[]{ccc}\hat{\theta}_{1}&\dots&\hat{\theta}_{n}\\\
\hat{A}_{1}&&\\\ &\ddots&\\\
&&\hat{A}_{n}\end{array}\right],\quad\hat{\beta}=\left[\begin{array}[]{c}B+\hat{\theta}^{\top}x^{\text{nom}}\\\
\hat{b}_{1}\\\ \vdots\\\ \hat{b}_{n}\end{array}\right]$

with
$\hat{\theta}^{\top}=[\begin{array}[]{ccc}\hat{\theta}_{1}&\dots&\hat{\theta}_{n}\end{array}]$.

  5. 5.

$\mathsf{P}$ proposes incentives $\gamma_{1},\dots,\gamma_{n}$ to the users
conditioned on the recommended emission-travel time outcomes
$x_{1}^{\text{rec}},\dots,x_{n}^{\text{rec}}$, respectively, which are
achieved by complying with the recommended routes and eco-driving strategies,
where

$\gamma_{i}=\hat{\theta}_{i}^{\top}(x_{i}^{\text{rec}}-x_{i}^{\text{nom}}).$

##  IV Experiments

###  IV-A Road Network

To test the proposed incentive mechanism, we set up a controlled experiment
with a simple road network using the Simulation of Urban MObility (SUMO) [11].
The road network consists of two routes for one origin-destination pair: the
first route through the urban area is shorter but includes two stop signs,
while the second route using a boulevard/highway, although longer, is
uninterrupted by stop signs (Fig. 2). The speed limit for both routes is set
to be the same. The first route, with two stop signs and one static traffic
signal, is shorter and takes less travel time, but it emits larger amounts of
carbon emissions because of stop-and-go traffic behavior. The second route is
longer and may take longer travel time, but it is more eco-friendly because of
smoother traffic.

OriginDestinationRoute 2 (Longer, via a boulevard)Route 1 (Shorter, via an
urban area) Figure 2: Illustration of the road network with two alternative
routes used in the simulation experiments.

###  IV-B Experiment Design

Building upon the road network, our experiment design is structured to analyze
the trade-offs between travel time and carbon emissions, directly informed by
the route choice for a given OD pair. We computationally generated free-flow
traffic conditions for both routes, ensuring an unbiased assessment of their
inherent characteristics. All vehicles follow the Intelligent Driver Model
(IDM), which is a time-continuous car-following model proposed by [12]. The
emission model used in the simulation is based on the Handbook Emission
Factors for Road Transport (HBEFA). Route 1, while shorter, was observed to
produce higher CO emissions because of the stops imposed by the stop signs and
a traffic signal. In contrast, Route 2, despite its longer distance, resulted
in lower emissions by benefiting from a continuous driving flow without
interruptions.

The collected data points, representative of the distinct travel times and
emissions outcomes for each route, helped construct a convex hull that
represents the feasible region of outcomes (Fig. 3). This convex hull is
instrumental in visualizing the potential impact of different driving
behaviors and route selections on travel time and carbon monoxide emissions.
For each type, the nominal (circle) and recommended (diamond) outcome points
are distinctly marked, providing insight into the specific eco-driving
recommendations by the incentive mechanism. This visual representation
underscores the emission-saving potential of Route 2 despite its longer travel
times, aligning with the eco-driving principles encouraged by the study’s
incentive mechanism. Our approach allows us to evaluate the effectiveness of
the proposed incentive mechanism in guiding drivers towards choices that align
better with eco-friendly driving principles.

Figure 3: The feasible set computed from the feasible outcome points of both
route 1 and 2. The nominal (circle) and recommended (diamond) outcome points
for the two driver types are also indicated. Nominal outcomes are what users
would generally opt for, while the recommended outcomes are suggested to users
by the eco-planner along with the incentives.

As described in Section II-D, we consider two incentive mechanisms: baseline
and optimal (proposed). In the baseline, we propose equal incentive
$\gamma_{i}^{\text{BL}}=B/n$ to all the users. Let $x_{i}^{\text{rec},r2}\in
X_{i}$ be a recommendation to users that corresponds to the least travel time
on feasible points corresponding to route 2. Then, user $i$ complies with this
recommendation under baseline incentive if and only if

$\gamma_{i}^{\text{BL}}\geq\theta_{i}^{\top}(x_{i}^{\text{rec},r2}-x_{i}^{\text{nom}}).$

Similarly, given budget $B$, the optimal incentive mechanism yields
$\gamma_{1},\dots,\gamma_{n}$, where the user $i$ complies with the
recommendation $x_{i}^{\text{rec},r2}$ if and only if

$\gamma_{i}\geq\theta_{i}^{\top}(x_{i}^{\text{rec},r2}-x_{i}^{\text{nom}}).$

###  IV-C Experimental Results

In Fig. 4, we illustrate the correlation between budget allocation and driver
compliance with eco-driving recommendations. It compares the result of the
linear program in (9) and baseline incentive across different budget levels.
It is apparent that under baseline incentives, compliance escalates swiftly
with a slight increase in budget, plateauing at a compliance ratio of 0.5.
Beyond this point, the compliance rate remains constant, indicating that
additional incentives under this model do not further motivate drivers. In
contrast, under optimal incentives, we observe a gradual yet consistent
increase in compliance as the budget grows, eventually surpassing the baseline
once half of the drivers are compliant. This trend suggests that the optimal
incentive structure is more effective at progressively encouraging a larger
proportion of drivers to adopt eco-driving practices, particularly in
scenarios where the budget is ample enough to support such incentivization.

Figure 4: Ratio of drivers complying with eco-driving recommendations under
different levels of budget.

Fig. 5 illustrates the relationship between the budget allocated for
incentives and the total CO emissions and average travel time from vehicles
within the simulation. Both are normalized for comparative purposes. The graph
compares the efficacy of baseline incentives to that of the proposed optimal
incentives. As shown in Fig. 5a, both incentive schemes initially cause a
sharp decrease in emissions as the budget is increased, demonstrating that
even minimal financial motivation can significantly alter driving behaviors.
However, the baseline incentives exhibit a more extended plateau compared to
the optimal incentives, indicating a point where additional funds cease to
yield proportional reductions in emissions. Conversely, the optimal incentives
lead to a more consistent and prolonged decline in emissions with increasing
budgets, highlighting their effectiveness in continuously promoting eco-
friendly driving practices. Meanwhile, Fig. 5b reveals an increase in average
travel time concurrent with efforts to reduce carbon emissions, emphasizing
the importance of a balanced strategy that judiciously weighs budget spending
against both environmental impact and time-savings.

(a) CO emission  (b) Average travel time

Figure 5: Comparison of CO emission and average travel time with different
levels of budget.

##  V Conclusion and Future Directions

To promote eco-driving in urban transportation networks, we have developed an
incentive mechanism in the form of a digital platform called eco-planner.
Before starting their trips, users report their origins, destinations, vehicle
types, and preferences for emissions versus travel time trade-offs. The eco-
planner then simulates different traffic conditions and driving styles to
generate optimal eco-driving recommendations and incentives for each user,
subject to a budget constraint. In other words, eco-planner guarantees certain
incentives to users who follow its recommendations. Users decide whether to
comply with the recommendations based on the incentives offered. At the end of
each trip, the eco-planner transfers the incentives to users who comply with
the recommendations and reduce their emissions.

Several features of the incentive mechanism are noteworthy. First, the
simulator efficiently computes the feasible outcomes for each user, helping
the eco-planner to optimally choose incentives for all users. Second, the
nominal outcomes of the users lie on the Pareto front of their feasible sets,
enabling the platform to compute each user’s incentive exactly using a simple
expression (5) depending on the corresponding recommendation.

Our future work includes modifying the incentive mechanism to be incentive-
compatible, meaning that strategic users cannot maximize their rewards by
reporting false information. Additionally, we will consider the effects of
non-participating traffic on eco-driving of the participating users. In this
scenario, the feasible sets computed by the platform may differ significantly
from the actual feasible sets of the users, due to different traffic
conditions and/or coupling between the driving behavior of users who share the
same routes. By addressing these challenges, we can improve our incentive
mechanism and make it more effective and suitable for deploying on real
transportation networks.

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