# Fairness-Enhancing Vehicle Rebalancing in the Ride-hailing System

Xiaotong Guo<EMAIL_ADDRESS>Hanyong Xu<EMAIL_ADDRESS>Dingyi Zhuang
<EMAIL_ADDRESS>Yunhan Zheng<EMAIL_ADDRESS>Jinhua Zhao, Ph.D<EMAIL_ADDRESS>Department of Civil and Environmental Engineering, Massachusetts Institute of
Technology, Cambridge, MA, USA  Department of Urban Studies and Planning,
Massachusetts Institute of Technology, Cambridge, MA, USA

###### Abstract

The rapid growth of the ride-hailing industry has revolutionized urban
transportation worldwide. Despite its benefits, equity concerns arise as
underserved communities face limited accessibility to affordable ride-hailing
services. A key issue in this context is the vehicle rebalancing problem,
where idle vehicles are moved to areas with anticipated demand. Without
equitable approaches in demand forecasting and rebalancing strategies, these
practices can further deepen existing inequities. In the realm of ride-
hailing, three main facets of fairness are recognized: algorithmic fairness,
fairness to drivers, and fairness to riders. This paper focuses on enhancing
both algorithmic and rider fairness through a novel vehicle rebalancing
method. We introduce an approach that combines a Socio-Aware Spatial-Temporal
Graph Convolutional Network (SA-STGCN) for refined demand prediction and a
fairness-integrated Matching-Integrated Vehicle Rebalancing (MIVR) model for
subsequent vehicle rebalancing. Our methodology is designed to reduce
prediction discrepancies and ensure equitable service provision across diverse
regions. The effectiveness of our system is evaluated using simulations based
on real-world ride-hailing data. The results suggest that our proposed method
enhances both accuracy and fairness in forecasting ride-hailing demand,
ultimately resulting in more equitable vehicle rebalancing in subsequent
operations. Specifically, the algorithm developed in this study effectively
reduces the standard deviation and average customer wait times by 6.48% and
0.49%, respectively. This achievement signifies a beneficial outcome for ride-
hailing platforms, striking a balance between operational efficiency and
fairness.

###### keywords:

Ride-hailing system, Vehicle Rebalancing, Fairness, Demand Prediction

##  1 Introduction

Since its introduction in 2009, the ride-hailing industry has witnessed
significant global growth. Fueled by technological advancements and the
widespread adoption of mobile phones, ride-hailing services offered by
Transportation Network Companies (TNCs) like Uber, Lyft, and Didi have
revolutionized commuting, creating new economic opportunities. With a market
size of approximately 30 billion USD and projected to reach 100 billion USD by
2030 [1], the industry continues to meet the increasing demand for convenient
and flexible transportation options in today’s rapidly urbanizing world.

However, alongside the benefits, the ride-hailing industry has also raised
significant societal concerns. Research conducted by Diao et al. [2] indicates
that the proliferation of TNCs has exacerbated urban mobility challenges,
resulting in increased road congestion and decreased usage of public transit.
Underserved communities and low-income neighborhoods have been
disproportionately affected by the limited accessibility and affordability of
ride-hailing services. Additionally, the heavy reliance on algorithms in TNC
platforms for tasks such as passenger-driver matching, pricing, and
operational optimization poses the risk of perpetuating biases and
discrimination if not designed and implemented with fairness in mind.

One of the major operational problems in the ride-hailing system is the
vehicle rebalancing problem, where vacant vehicles are redistributed
proactively to undersupplied areas to reduce the discrepancy between supply
and demand [3, 4, 5, 6, 7, 8]. Nevertheless, if ride-hailing platforms focus
solely on maximizing profits or efficiency without considering equity
concerns, their operational approach can trigger a detrimental feedback loop
within the system.

Consider the case of New York City (NYC). As illustrated in Figure 1, the map
displays the spatial distribution of ride-hailing demand and poverty levels in
the city. Darker shades represent areas with a higher population living below
the poverty line and lower ride-hailing demand. Predictably, regions with a
larger impoverished population exhibit reduced ride-hailing demand, such as
upper Manhattan, the Bronx, and lower Brooklyn. During the process of
redistributing vacant vehicles to meet demand, vehicles tend to be reallocated
to high-demand regions, which are more likely to receive future passenger
requests. This redistribution, however, diminishes the supply and service
levels in low-demand areas, typically inhabited by people facing poverty.
Consequently, residents in these low-demand regions are discouraged from using
ride-hailing services when the service levels decrease. This negative feedback
loop exacerbates the situation, limiting ride-hailing options to affluent
individuals and exacerbating serious equity issues.

(a) NYC Ride-Hailing Demand Distribution (by taxi zones)

(b) NYC Poverty Map (by census tracts)

Figure 1: Spatial distributions of ride-hailing demand and poverty in New York
City (NYC).

Moreover, accurate short-term travel demand forecasting is essential for
efficient vehicle rebalancing in ride-hailing systems. Data-driven approaches,
including traditional time series analysis [9, 10] and modern machine learning
models [11, 12, 13, 14, 15, 16], have been utilized in generating reliable
predictions. However, many studies focus solely on prediction accuracy,
disregarding the social consequences of travel demand forecasting. Take the
vehicle rebalancing problem for instance, under-predicting travel demand in
disadvantaged neighborhoods can result in fewer vehicles being dispatched to
the area, leading to inadequate services for certain groups.

Hence, we pinpoint two key fairness concerns in ride-hailing system vehicle
rebalancing: firstly, the strategies employed prioritize profit and efficiency
at the expense of equity considerations, and secondly, the prediction
algorithms essential for rebalancing operations may give rise to algorithmic
fairness problems. In this paper, we outline two levels of fairness aimed at
improvement:

  1. 1.

Fairness in Provisioned Ride-Hailing Services: Our goal is to reduce
disparities in services provided by customers, regardless of the regions from
which trips originate.

  2. 2.

Fairness in Demand Prediction Algorithms: We aim to minimize prediction errors
for each region, irrespective of spatial locations and historical demand
levels, involved in vehicle rebalancing operations.

Prior research in the ride-hailing domain has been predominantly focused on
enhancing particular facets of fairness: algorithmic fairness, driver
fairness, and rider fairness. Notably, algorithmic fairness has been addressed
in demand prediction efforts by Yan and Howe [17, 18], Zheng et al. [19].
Fairness concerning driver earnings has been explored by Sühr et al. [20],
Bokányi and Hannák [21], Sun et al. [22]. Additionally, fairness in the
service and pricing offered to riders has been discussed in studies by Nanda
et al. [23], Lu et al. [24], Ke and Qian [25]. However, it is rare for studies
to integrate more than two dimensions of fairness. Cao et al. [26] has
contemplated both the fairness of drivers’ income and the fairness to riders
concerning varying detour distances. Similarly, Raman et al. [27] has
considered income disparity among drivers as well as the differential
treatment of riders based on socio-demographic factors. Nevertheless,
algorithmic fairness typically receives attention as a standalone issue. To
the best of authors’ knowledge, there have yet to be studies that concurrently
address the concerns of algorithmic fairness and rider fairness within the
context of ride-hailing systems.

This study introduces a fairness-enhancing vehicle rebalancing framework,
taking into account both the algorithmic fairness in demand prediction and the
fairness of services provided to riders in the downstream vehicle rebalancing
operation, building upon the Matching-Integrated Vehicle Rebalancing (MIVR)
algorithm [7]. The framework aims to tackle the two levels of fairness
outlined previously. The key contributions of this paper are summarized as
follows:

  * •

This work represents a novel contribution to the realm of ride-hailing vehicle
rebalancing by aiming to advance fairness in the realms of both demand
prediction and the provision of services to riders in various regions.

  * •

We introduce a Socio-Aware Spatial-Temporal Graph Convolutional Network (SA-
STGCN) that builds upon the STGCN model [28], enhancing upstream demand
prediction. This new framework incorporates a socio-enriched adjacency matrix
and a bias-mitigation regularization method to minimize prediction
discrepancies across regions.

  * •

Building on the MIVR algorithm, we enhance the vehicle rebalancing process
with a fairness-focused weighted objective function. This function is informed
by the socio-enriched adjacency matrix derived from the SA-STGCN model.

  * •

We implement several fairness metrics to evaluate the accuracy of demand
prediction algorithms and utilize real-world ride-hailing data to test the
fairness of the services provided to riders. Our framework is designed to
mitigate fairness issues in both the prediction of demand and the distribution
of services to riders.

The remainder of this paper is organized as follows. Section 2 provides a
comprehensive review of the existing literature on ride-hailing vehicle
rebalancing problems, demand prediction approaches, and fairness issues within
the ride-hailing system. In Section 3, we present the fairness-enhanced
vehicle rebalancing framework. The results of our numerical experiments are
presented in Section 4. Section 5 discussed the policy implications from the
results. Finally, Section 6 summarizes the paper and outlines future research
directions.

##  2 Literature Review

###  2.1 Ride-Hailing System and Vehicle Rebalancing Problem

The field of ride-hailing systems is extensively studied, as outlined in
sources like Wang and Yang [29]. This body of research covers a range of
topics including the structure of the market [30, 31, 32], analyses of labor
supply [33], operations of matching drivers with passengers [34], strategies
for vehicle rebalancing [3, 4, 5, 6, 7, 8], designs of surge pricing [35],
among other areas. A key operational strategy in these systems is the
rebalancing of vacant vehicles. This process is vital in complementing the
primary function of connecting customers with available drivers.

A major challenge in ride-hailing systems is the spatial mismatch between
where demand arises and where vehicles are available. To address this, there’s
a need for relocating idle vehicles to areas where future demand is
anticipated to exceed the current supply of vehicles. By adopting this
proactive rebalancing approach, ride-hailing platforms can significantly
reduce the distance traveled by empty vehicles, also known as ’empty miles’,
and concurrently decrease the waiting times for customers. This strategy is
essential for optimizing operational efficiency and enhancing user
satisfaction in ride-hailing services.

The vehicle rebalancing problem is initially studied by Godfrey and Powell
[36, 37] under the context of dynamic fleet management. Over the past decade,
with the rapid growth of Mobility-on-Demand (MoD) and ride-hailing systems,
more attention has been devoted to solving this challenge [6, 38, 39, 5]. Wen
et al. [6] used reinforcement learning to tackle vehicle rebalancing in a
shared MoD system, achieving a 14% fleet size reduction in a London
simulation. Braverman et al. [39] designed a fluid-based optimization model
for ride-hailing vehicle management, resulting in improved passenger service
compared to benchmark models. Miao et al. [5] introduced a data-driven vehicle
rebalancing model, minimizing the worst-case rebalancing cost using real-world
NYC taxi data, achieving an average 30% reduction in idle driving distance.
Guo et al. [7] proposed the Matching-Integrated Vehicle Rebalancing (MIVR)
model for solving the vehicle rebalancing problem considering future
iterations and incorporated the demand uncertainty with the Robust
Optimization (RO) techniques. Guo et al. [8] expanded on this concept by
exploring multiple data-driven strategies to handle demand uncertainty within
the framework of the MIVR model.

Meanwhile, various studies have been focused on the control of Autonomous MoD
system [40, 41, 42, 43, 44], where vehicles are dispatched in the system by
the proposed control strategy. Pavone et al. [41] used a fluid-based model and
linear program for generating optimal rebalancing policy. Zhang and Pavone
[42] proposed a queueing-based algorithm for AMoD rebalancing. Iglesias et al.
[43] utilized LSTM neural networks in a Model Predictive Contro (MPC)
algorithm for rebalancing with short-term demand forecasts. Tsao et al. [44]
further introduced an MPC algorithm in the shared AMoD setting.

Despite the extensive research on vehicle rebalancing, none of the existing
studies have explicitly tackled equity concerns in their proposed algorithms.
This paper aims to fill this gap by presenting a fairness-enhanced vehicle
rebalancing framework building upon the MIVR model [7] that systematically
addresses issues related to the perceived services experienced by customers.

###  2.2 Demand Prediction in the Transportation System

Predicting the accurate travel demand of a given transportation system is
crucial for efficient traffic operations and regulations. A great volume of
research has studied diverse methods for travel demand forecasts. Traditional
common methods include the Historical Averages, Moving Averages,
autoregressive integrated moving average (ARIMA) and its variants, and some
basic machine learning models such as support vector machines (SVM) [9, 45,
46, 47]. However, these models focused more on temporal links but failed to
account for spatial and relational information in the transportation network
[46].

In recent years, with the rise of large machine learning models and the
booming computing power, there has been a shift from using traditional
statistical time series analysis to deep learning sequential networks [47].
Many studies have leveraged the convolutional neural networks (CNN) such as
ResNet to capture spatial features [48, 49] and used the recurrent neural
networks (RNN) such as the long-short term memory (LSTM) and Attention
mechanism to learn the time series function [50, 13, 51].

On the other hand, graph neural networks (GNN) gained popularity because of
their ability to capture spatial dependency and the non-Euclidean structure of
the street network [52]. There are many types of graph convolutions in GNNs,
including the spectral-based graph convolutional networks (GCN) [53, 54] and
spatial-based convolutional GNNs [55, 56, 57, 58]. Many architectures are
proposed to solve traffic forecasting problems. For instance, Li et al. [59]
proposed the Diffusion Convolutional Recurrent Neural Network (DCRNN),
leveraging bidirectional graph random walk and the recurrent neural network to
capture both the spatial and temporal dependencies. Yu et al. [28] proposed
the Spatial-Temporal Graph Convolutional Network (STGCN), using graph and
temporal convolution layers to build up the basic block of the architecture.
Wu et al. [60] developed the Graph WaveNet, which utilized a self-adaptive
adjacency matrix to capture hidden relations in the graph and leveraged
dilated causal convolution to work with long-range sequences. Our research
adopted the STGCN model as the main structure for its state-of-art performance
and ease of implementation.

###  2.3 Fairness in the Transportation System

####  2.3.1 Fairness Definition

There is a wide range of debates regarding the definition of fairness in
political philosophy, computer science, and transportation. Major theories of
fairness in political philosophy can be separated into four categories, which
are 1) ensure equal share or proportional share for each individual, 2) ensure
market equilibrium, 3) maximize total welfare, and 4) ensure subgroup welfare
[61, 62]. In computer science, there are also various evaluation metrics to
measure algorithmic fairness, the first set is Disparate Impact Analysis
versus Disparate Treatment Analysis, where the former aims to achieve fair
impact or results for the unit of comparison while the latter aims to achieve
fair treatment [63, 64]. Another set of evaluation notions based on the unit
of comparison includes group-based and individual-based fairness, where the
former focuses on the same outcome or treatment of different groups, while the
latter concentrates on the same outcome or treatment of individuals [65, 63].
In transportation, horizontal equity and vertical equity are often alluded to.
Horizontal equity refers to the goal of similar people receiving similar
treatment, while vertical equity refers to the goal of disadvantaged people
being taken care of [66, 17]. This fairness notion aligns with the many
existing concepts of fairness and equity from the fields of political
philosophy and computer science.

####  2.3.2 Fairness Research in the Transportation System

Research in fairness and equity in the transportation system has been emerging
in recent years, especially in public transit planning, where the fair sharing
of public resources is important. Previously, a lot of the focus was put on
the equity analysis of the existing or forthcoming systems. Bills and Walker
[67] measured and compared consumer surplus distributions for different
population segments across planning scenarios in the Bay area. Cascetta et al.
[68] estimated the horizontal equity of the travel time accessibility by
calculating the Gini index for Italian high-speed railways. On the other hand,
Zheng et al. [69] demonstrated the unfairness in the Deep Neural Network and
the Discrete Choice Model, unlike preceding research, they also provided a
disparity mitigation solution through an absolute correlation regularization
method.

In the realm of ride-hailing, researchers have been focused on improving
algorithmic fairness, driver fairness, and rider fairness. Yan and Howe [17]
addressed the challenge of socio-economic inequity perpetuated by new mobility
services like car-sharing, bike-sharing, and ride-hailing. Yan and Howe [18]
discussed a novel unsupervised learning architecture, named EquiTensors, for
integrating heterogeneous spatio-temporal urban data to counteract bias and
produce fair and reusable representations. Both Zheng et al. [19] and Zhang et
al. [70] have looked at the demand prediction fairness in ride-hailing,
however, they only leveraged group fairness as a fairness definition and
focused on the prediction result without considering the downstream impact.

In exploring driver-side fairness in ride-hailing systems, various studies
have made significant contributions. Bokányi and Hannák [21] employed a city
simulation to highlight critical issues of fairness and wage inequality. Sühr
et al. [20] analyzed drivers’ income fairness over time, suggesting a
framework that enhances the utility for both customers and drivers in a dual-
sided market. Sun et al. [22] tackled the dual challenge of efficiency and
fairness, introducing a multi-agent reinforcement learning framework that
assists drivers in making equitable income decisions through order selection
and repositioning. Raman et al. [27] offered two strategies within a Markov
decision process to mitigate inequality in ride-pooling services, aiming to
balance profitability and fairness for both passengers and drivers.

As for rider-side fairness in transportation systems, Qian et al. [71]
developed a novel route recommendation system that considers shared roads
while maintaining cost-effectiveness for each customer. Cao et al. [26] aimed
at enhancing both efficiency and fairness in ride-sharing by optimizing routes
for ride-hailing services. Ke and Qian [25] introduced the concept of Fleet-
Optimal Behavior with Service Constraint (FOSC), focusing on striking a
balance between reducing total fleet costs and ensuring fair travel times for
riders. Nanda et al. [23] proposed a driver-customer matching algorithm that
addresses the challenge of maximizing profit while maintaining fairness in
rider matching rates. Lu et al. [24] suggested a decentralized smart price
auditing system using block-chain technology and smart contracts to ensure
price fairness and prevent discrimination among riders in ride-hailing
services.

In this paper, we present a new vehicle rebalancing framework aimed at
simultaneously enhancing algorithmic and rider fairness, aspects not jointly
considered in existing research. This innovative approach ensures equitable
and efficient operations, setting a new standard for fairness in vehicle
rebalancing.

##  3 Methodology

In this section, we will introduce the fairness-enhancing vehicle rebalancing
framework, consisting of a Socio-Aware STGCN (SA-STGCN) demand prediction
component and a fairness-enhancing MIVR component for downstream vehicle
rebalancing operations.

###  3.1 Fairness-Enhancing Demand Prediction Framework

The original STGCN (Spatio-Temporal Graph Convolutional Network) framework,
while effective in numerical prediction accuracy, primarily concentrated on
leveraging spatial locality information and temporal autocorrelations. This
approach, though beneficial in certain contexts, inadvertently leads to a
regional imbalance in the model outputs. Such imbalances can propagate
unfairness in downstream applications, particularly in tasks that are
sensitive to regional disparities. Recognizing this limitation, our research
proposes the innovative SA-STGCN (Social Aware STGCN) framework, complemented
by a fairness-enhancing methodology specifically tailored for vehicle
rebalancing optimization in ride-hailing operations. The conceptual
architecture of this approach is detailed in Figure 2:

Figure 2: Detailed illustrations of the SA-STGCN framework and its integration
with the vehicle rebalancing optimization task.

As depicted in Figure 2, our modifications to the STGCN framework are
multifaceted and designed to address the fairness issue at its core. These
modifications include:

  1. 1.

Implementing a fairness-enhanced loss regularization approach to penalize
demand overestimations and reduce output disparities.

  2. 2.

Integrating a demographic matrix (e.g., representing the Black and low-income
population) with the original adjacency matrix to infuse social context into
the data.

  3. 3.

Employing matrix decomposition on the augmented adjacency matrix to derive
demographic weights, which serve as adjustment factors in the downstream
rebalancing task.

In the following sections, we delve deeper into each of these components,
discussing their implementation and the specific methodologies employed. We
aim to provide a comprehensive understanding of how each aspect contributes to
the overall effectiveness and fairness of the SA-STGCN framework.

####  3.1.1 Socio-Aware Spatial-Temporal Graph Convolutional Network

This module starts by formulating the demand prediction problem. Given the
ride-hailing system, we can regard it as a directed weighted graph
$G=(V,E,W)$, where $|V|=n$ is the set graph vertices representing sub-regions
(zones), the $E$ represents the set of road networks between each pair of
vertices as edges, and $W$ represents the weights of each edge in the form of
weighted adjacency matrix, calculated by:

$W_{ij}=\exp{(-\frac{\bar{d}_{ij}^{2}}{\sigma_{d}^{2}})},$ (1)

where $W_{ij}$ is the edge weight between graph vertices $v_{i}$ and $v_{j}$,
$\bar{d}_{ij}$ is the Euclidean distance between the centroids of vertices
$v_{i}$ and $v_{j}$, $\sigma_{d}$ is the standard deviation of the set of
distances begins at each vertex $v_{i}$ [54].

To capture the spatial demographic features that exist in the network, this
study establishes a socio-demographically enriched adjacency matrix by
incorporating an additional demographic matrix. In this study, we leverage
census data and focus on the ratio of the minority race population and the
population in poverty as the variables of interest. The first step is to
construct a demographic matrix. Consider the demographic variables in
preceding $N$ years in each graph vertice $v_{i}$ as a vector $z_{i}$ where
$|z_{i}|=2N$ since we only focused on two variables here. Then we can
construct the relationship between the demographic features of each pair of
vertices $z_{i}$ and $z_{j}$ with a correlation matrix.

$Corr_{ij}=\frac{\sum^{2N}_{m=1}(z^{m}_{i}-\bar{z_{i}})(z^{m}_{j}-\bar{z_{j}})}{\sqrt{\sum^{2N}_{m=1}(z^{m}_{i}-\bar{z_{i}})^{2}}\sqrt{\sum^{2N}_{m=1}(z_{j}-\bar{z_{j}})^{2}}},$
(2)

where $z^{m}_{i}$ and $z^{m}_{j}$ are the individual elements in $z_{i}$ and
$z_{j}$. When $z_{i}$ = $z_{j}$ = 0, the corresponding value in the matrix
will be filled as zero.

We derived a new socio-demographically adjacency matrix that incorporates this
demographic matrix into the original adjacency matrix, specifically, we use
the Hadamard product of the original adjacency matrix and the demographic
correlation matrix as the new adjacency matrix to feed into the prediction
model described below. To introduce sparsity, the element value of the new
matrix is only kept when it is greater than or equal to 0.1, otherwise, it is
converted to 0.

$W_{ij}^{*}=\begin{cases}W_{ij}\circ Corr_{ij},&\text{if }W_{ij}\circ
Corr_{ij}\geq 0.1,\\\ 0,&\text{otherwise}.\end{cases}$ (3)

In terms of the representation of the ride-hailing demand, let
$r_{i}^{k}\in\mathbb{N}$ be the demand at each time period $k$ that originates
at vertex $v_{i}$ (or sub-region $i$). Given the demand observations from
previous $M$ time periods at each vertex $[r^{k-M},...,r^{k-1}]$, we want to
forecast the upcoming demand $\hat{r}^{k+1}$.

The study refers to the Spatial-Temporal Graph Convolutional Network (STGCN)
proposed by [28] as the main model structure. STGCN has been widely used in
traffic forecasting for its excellent ability to capture temporal and spatial
features compared to traditional CNN and time-series models because it
utilizes both graph and gated temporal convolutions. The model we adopted
consists of two Spatial Temporal Convolutional (ST-Conv) blocks followed by a
fully connected layer. Each ST-Conv block comprises two temporal gated
convolution layers and a spatial graph convolution layer in between. To reduce
the computing cost of graph convolution, we adopted the Chebyshev Polynomials
Approximation and the 1st-Order Approximation strategies [54, 53, 28].

####  3.1.2 Fairness Enhancement

This research takes the individual fairness definition mentioned previously as
the objective. In this study, we addressed the fairness issue with
regularization inspired by the work of [19] and [72] and applied three
versions of fairness cost terms in the cost function. The set of demand
predictions $\hat{R}$ and all the trainable parameters in the model
$W_{\theta}$ gives the cost function. In general, the cost function consists
of two parts, each optimizes the accuracy and the fairness of the model
performance:

$J_{total}=J_{accuracy}+param*J_{fariness},$ (4)

where $param$ is a hyperparameter that adjusts the relative weight of the
fairness optimization term. The research uses $\lambda$ and $\gamma$ as the
weight parameter for the case of limiting error distribution and penalizing
overestimation, respectively.

Limit error distribution. To achieve fairness for the whole population and
regulate the error distribution variance, we add the variance of the symmetric
absolute percentage error (SAPE) to the cost function. First, $SAPE$ at each
vertex in a given time period is defined as:

$SAPE_{i}^{k}=\begin{cases}\frac{|r_{i}^{k}-\hat{r}_{i}^{k}|}{|r_{i}^{k}|+|\hat{r}_{i}^{k}|},&|r_{i}^{k}|+|\hat{r}_{i}^{k}|\neq
0,\\\ 0,&\text{otherwise},\end{cases}$ (5)

where $r_{i}^{k}$ and $\hat{r}_{i}^{k}$ are the original demand and the
predicted demand in vertex $v_{i}$ at time $k$. Measuring the percentage error
in this way is useful in the case of ride-hailing as the prediction and
original demand are sometimes equal or close to zero, making the traditional
percentage error term fraction undefined. In the case where both the
prediction and original demand are zero, we set the error term as zero. Then,
we can calculate the variance of the $SAPE$ for all vertices in a given time
period to the cost function:

$J(\hat{R},W_{\theta})=\sum_{k=1}^{\kappa}\sum_{i=1}^{n}(r_{i}^{k}-\hat{r}_{i}^{k})^{2}+\lambda\sum_{k=1}^{\kappa}\frac{\sum_{i=1}^{n}(SAPE_{i}^{k}-\bar{SAPE^{k}})^{2}}{n-1},$
(6)

where $\kappa$ is the number of time periods in each training iteration.

Penalize overestimation. As Guo et al. [8] pointed out in their study of ride-
hailing vehicle rebalancing operations, when the model prediction is not
accurate enough, underestimation is preferred compared to overestimation
because this avoids unnecessary vehicle relocation, resulting in a better
rebalancing result. Moreover, the resultant smaller overestimation will help
to reduce the total variance of the prediction error, thus providing a fairer
outcome. To reduce overestimation, we add a penalizing term to the cost
function:

$J(\hat{R},W_{\theta})=\sum_{k=1}^{\kappa}\sum_{i=1}^{n}(r_{i}^{k}-\hat{r}_{i}^{k})^{2}+\gamma\sum_{t=1}^{\kappa}\sum_{i=1}^{n}max(0,\hat{r}_{i}^{k}-r_{i}^{k}).$
(7)

In this way, whenever the prediction overestimates the demand, that is, when
$\hat{r}_{i}^{k}>r_{i}^{k}$, the regularization term will penalize it to be
closer to zero.

Limit error distribution and penalize overestimation. Lastly, we combine the
previous two regularizations together to achieve the effect of both limiting
error distribution and penalizing overestimation:

$J(\hat{R},W_{\theta})=\sum_{t=1}^{\kappa}\sum_{i=1}^{n}(r_{i}^{k}-\hat{r}_{i}^{k})^{2}+\lambda\sum_{k=1}^{\kappa}\frac{\sum_{i=1}^{n}(SAPE_{i}^{k}-\bar{SAPE^{k}})^{2}}{n-1}+\gamma\sum_{k=1}^{\kappa}\sum_{i=1}^{n}max(0,\hat{r}_{i}^{k}-r_{i}^{k})$
(8)

####  3.1.3 Weighted Adjacency Matrix Decomposition

The first two components of the SA-STGCN framework focus on addressing
fairness concerns in demand prediction. This section introduces a matrix
decomposition method to create fairness weights for sub-regions, indicating
the importance of repositioning idle vehicles to each sub-region. This vector
is then applied in the subsequent vehicle rebalancing task, aiming to enhance
fairness in the delivery of ride-hailing services.

In order to obtain the fairness weights of different regions to guide the
downstream rebalancing task, we decomposed our self-designed adjacency matrix
to obtain a set of fairness weights that consider both the spatial
dependencies as well as the disparity of socio-demographic features in the
city. Therefore, two consecutive steps are conducted through the process: (1)
Enrich the weighted adjacency matrix $W$ with sociodemographic information,
which was explained by Equation 2 and 3; (2) Decompose the adjacency matrix to
obtain the spectrum and use it as the output weights, which will be explained
in this section.

The decomposition of the adjacency matrix is usually applied in the graph
spectrum analysis because it provides a powerful means to reveal and quantify
the latent structural properties of graphs, such as node centrality, community
structure, and connectivity patterns [73, 74]. In our context, we use
Canonical polyadic (CP) decomposition in our experiment. The CP decomposition,
also known as PARAFAC or tensor factorization, is a multilinear algebraic
framework that generalizes the matrix singular value decomposition to higher-
order tensors [75, 76, 77]. For our adjacency matrix $W^{*}$, viewed as a two-
dimensional tensor, CP decomposition factorizes $W^{*}$ into a sum of
component rank-one tensors, providing insights into multi-way interactions.
Mathematically, if $W^{*}$ is a tensor of order two, the CP decomposition is
represented as:

$W^{*}\approx\sum_{r=1}^{R}\lambda_{r}\mathbf{a}_{r}\otimes\mathbf{b}_{r},$
(9)

where $\otimes$ denotes the outer product, $R$ is the rank of the
decomposition, $\lambda_{r}$ are the weights indicating the importance of each
component, and $\mathbf{a}_{r}$ and $\mathbf{b}_{r}$ are the corresponding
factor vectors representing the demographic modes and weights of the
decomposed $W^{*}$. This decomposition facilitates the distillation of complex
network data into a form that accentuates inherent spatial and
sociodemographic relationships, allowing for compressing $W^{*}$ to capture
nuanced regional disparities in a comprehensible manner. In this study, we
define $R=1$ to produce a pair of vectors that encapsulate the maximum amount
of information from the adjacency matrix $W^{*}$.

The fairness weights for the downstream optimization problem will be derived
from the vector $\boldsymbol{b}$ by following these procedures: i) Normalize
$\boldsymbol{b}$ using a min-max scaling method, ii) decrease the magnitude of
each element by multiplying with 0.1, and iii) obtain the final fairness
weights for each sub-region by subtracting each scaled value from 1.
Specifically, for each sub-region $i$, the normalized value $\bar{b_{i}}$ is
computed as

$\bar{b_{i}}=\frac{b_{i}-\min(\boldsymbol{b})}{\max(\boldsymbol{b})-\min(\boldsymbol{b})}.$

Subsequently, the fairness weight for each sub-region $i$ is determined as

$\omega_{i}=1-0.1\times\bar{b_{i}}.$

Our enriched adjacency equation (Equation 3.1.1) indicates that sub-regions
nearer to other sub-regions, with lesser poverty rates and smaller minority
race populations, are likely to have higher $b_{i}$ values. In contrast, city
outskirts, typically marked by higher poverty and more significant minority
race populations, are distinct from urban centers. The aim of the fairness
weights is to prioritize these underserved peripheral areas, which often face
greater socio-economic challenges. These weights are calculated following the
earlier mentioned steps, ensuring that sub-regions with elevated $b_{i}$
values correspondingly have lower $\omega_{i}$ values, thus aligning with our
objective of equitable distribution.

###  3.2 Fairness-Enhancing Vehicle Rebalancing Component

Tackling fairness concerns in the demand prediction module doesn’t directly
mitigate fairness issues related to the services received by customers, who
are the primary indicators when evaluating ride-hailing operations. Therefore,
this provides a fairness-enhancing Matching-Integrated Vehicle Rebalancing
(MIVR) model, building upon the MIVR model proposed by Guo et al. [7].

The operational period is divided into $\Omega$ identical time intervals, each
denoted by an index $k=1,2,...,\Omega$, and lasting $\Delta$ time units.
Furthermore, the study area is partitioned into $n$ sub-regions (zones), with
each sub-region $i$ exhibiting an estimated demand $r_{i}^{k}\geq 0$ at time
$k$. To formulate the model, we introduce two sets: i) the set of sub-regions
denoted as $N={1,2,...,n}$, and ii) the set of time intervals represented by
$K={1,2,...,\kappa}$.

The MIVR model is solved in a rolling-horizon manner: when solving the MIVR
model at the start of time interval $k$, it considers the demand during time
interval $k$ as well as the demand for $\kappa$ future time intervals;
however, only the vehicle rebalancing decisions for the current time interval
$k$ are put into action; following this, vehicle locations are observed and
updated as inputs to the MIVR model for the subsequent time interval.

The MIVR model consists of two components: matching and rebalancing. The
matching component uses decision variables $y_{ij}^{k}\in\mathbb{R}^{+}$ to
represent the number of customers matched between sub-regions $i$ and $j$ at
time $k$. The rebalancing component uses decision variables
$x_{ij}^{k}\in\mathbb{R}^{+}$ to denote the number of idle vehicles rebalanced
from sub-region $i$ to sub-region $j$ at time $k$. Travel distance
$d_{ij}^{k}$ between sub-regions $i$ and $j$ at time $k$ is approximated by
the distance between their centroids.

The fairness considerations are incorporated by introducing the fairness
weights $\boldsymbol{\omega}\in(\mathbb{R}^{+})^{n}$, consisting of a weight
parameter $\omega_{i}$ for each region $i$. The fairness weights
$\boldsymbol{\omega}$ are decomposed from the enriched adjacency matrix from
the SA-STGCN framework. The weighted objective function of the MIVR model can
then be formulated as

$\displaystyle\small\min_{\boldsymbol{x},\boldsymbol{y}}\quad$ $\displaystyle
c(\boldsymbol{x},\boldsymbol{y};\boldsymbol{r})=\sum_{k=1}^{\kappa}\sum_{i=1}^{n}\sum_{j=1}^{n}x_{ij}^{k}d_{ij}^{k}+\alpha\cdot\sum_{k=1}^{\kappa}\sum_{i=1}^{n}\sum_{j=1}^{n}\omega_{i}y_{ij}^{k}d_{ji}^{k}+\beta\cdot\sum_{k=1}^{\kappa}\sum_{i=1}^{n}\omega_{i}\left(r_{i}^{k}-\sum_{j=1}^{n}y_{ij}^{k}\right),$
(10)

where $\boldsymbol{r}$ stands for the vector of estimated demand, $\alpha$ and
$\beta$ are weight parameters indicating weights for matching distance and
penalty for unsatisfied demand, respectively. The objective function
$c(\boldsymbol{x},\boldsymbol{y};\boldsymbol{r})$ defines a weighted
generalized cost for the vehicle rebalancing problem with the consideration of
the matching component. The fairness weights $\boldsymbol{\omega}$ play a
crucial role in rebalancing decisions by imposing extra costs and penalties on
specific regions, thereby guiding vehicles towards these areas. The
constraints used in this optimization problem can be found in Guo et al. [7].

With a given demand prediction $\boldsymbol{r}$, problem 10 provides a vehicle
rebalancing strategy for the upcoming decision time interval. The demand
prediction $\boldsymbol{r}$ is provided by the upstream SA-STGCN framework,
which balances the prediction accuracy and fairness metrics.

##  4 Experimental Results

###  4.1 Data

This research utilizes For-Hire Vehicle trip records obtained from the NYC
Taxi and Limousine Commission [78]. The experiments are conducted using “taxi
zones”, which are well-defined regions within the high-volume ride-hailing
trip dataset, comprising a total of 63 zones on Manhattan Island.

To best emulate typical travel behaviors, five months of demand data from
February to June 2019 are utilized, encompassing a total of 47,009,841 trips
within the study period. The demand data is aggregated into 5-minute time
intervals ($\Delta=300$ seconds) for analysis and evaluation. Figure 3
illustrates the average and standard deviation of daily regional demand in
Manhattan, revealing significant demand volatility in the lower Manhattan
area.

(a) Mean

(b) Standard deviation

Figure 3: Daily demand by zone (trips) in Manhattan.

In the demand prediction module, these taxi zones are employed as vertices in
the graph $G$. The dataset is divided into three subsets: the training set,
validation set, and test set, which account for 70%, 15%, and 15% of the
overall dataset, respectively. To predict the demand $r^{k}$ for a given taxi
zone at time $k$, the module utilizes the previous 12 observations of demand
$[r^{k-12},r^{k-11},...,r^{k-1}]$.

To assess the performance of both the demand prediction and vehicle
rebalancing modules, real-world demand data from June 26, 2019, is used as the
evaluation set. This one-day demand data is excluded from the training stage
to ensure a fair assessment of the modules’ capabilities.

To incorporate the socio-demographic information into both the upstream
prediction and downstream operation, we used the American Community Survey
(ACS) census data. Specifically, we focused on two variables, the racial and
poverty compositions of a given region to represent the population vulnerable
to insufficient ride-hailing service provision. The poverty level is pre-
determined by the ACS dataset. We also selected five years of data from
2015-2019 to capture a fuller picture of the demographic patterns in the city.
Figure 4 illustrates the spatial distributions of the two variables in 2019.
There is apparent spatial clustering concerning how the marginalized
population resides in the city. The original census data is at the census
tract level, and to aggregate it to the taxi zone level for future estimation,
we calculated the centroid of each census tract, assigned them to the
corresponding taxi zone, and summed up the population of each demographic
variable in each taxi zone. To calculate the ratio of each demographic, we
divided the population of the target demographic population by the total
population for each taxi zone.

(a) Black Population Ratio

(b) Poverty Population Ratio

Figure 4: Demographic Variables Distribution in Manhattan in 2019.

###  4.2 Performance Evaluation

####  4.2.1 Upstream Prediction Evaluation

The study adopted two sets of metrics to evaluate the accuracy and fairness of
the models respectively. To measure accuracy, we measured the error magnitude,
relative error percentage, and error direction. Two commonly used metrics,
Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), are adopted to
evaluate error magnitude. They are defined as follows:

$MAE=\frac{1}{\kappa\times
n}\sum_{k=1}^{\kappa}\sum_{i=1}^{n}|r_{i}^{k}-\hat{r}_{i}^{k}|,$ (11)
$RMSE=\sqrt{\frac{1}{\kappa\times
n}\sum_{k=1}^{\kappa}\sum_{i=1}^{n}(r_{i}^{k}-\hat{r}_{i}^{k})^{2}}.$ (12)

In addition, to measure the relative error percentage, we adopted the Mean
Absolute Percentage Error (MAPE):

$MAPE=\frac{1}{\kappa\times
n}\sum_{k=1}^{\kappa}\sum_{i=1}^{n}\frac{|r_{i}^{k}-\hat{r}_{i}^{k}|}{r_{i}^{k^{\prime}}}\text{,
where }r_{i}^{k^{\prime}}=min(r_{i}^{k},0.1).$ (13)

Note that the denominator $r_{i}^{k^{\prime}}$ is adjusted to ensure the
fraction is defined. Lastly, to measure the overall prediction error direction
compared to the original demand, we adopted the Mean Error (ME):

$ME=\frac{1}{\kappa\times
n}\sum_{k=1}^{\kappa}\sum_{i=1}^{n}(r_{i}^{k}-\hat{r}_{i}^{k}),$ (14)

where a positive ME value denotes the model underestimating the demand in
general, and vice versa.

On the other hand, to evaluate the fairness of the model predictions, we
utilized two metrics. The first metric is the Mean-Variance of the Percentage
Error (MVPE). This metric originates from the goal to ensure equal error
distribution for all predictions. Given the percentage error in vertex $i$ at
time $t$, $PE_{i}^{k}=\frac{r_{i}^{k}-\hat{r}_{i}^{k}}{r_{i}^{k}}$, the MVPE
is defined as:

$MVPE=\frac{1}{\kappa}\sum_{k=1}^{\kappa}\frac{\sum_{i=1}^{n}(PE_{i}^{k}-\bar{PE^{k}})^{2}}{n-1}$
(15)

where $\bar{PE^{k}}$ is the mean of the percentage errors in a given period
$k$.

The second fairness metric refers to the Generalized Entropy Index proposed by
[79]. It is a metric originated from economics that measures inequality, or in
the point of information theory, it can be interpreted as the $redundancy$ in
data. In our case, it measures the spread between individual prediction and
the average prediction error. A smaller value represents a more even
distribution between errors and their mean. We adjusted the metric to evaluate
the distribution of the percentage errors in our research setting:

$\displaystyle b_{i}^{k}=PE_{i}^{k}+m\text{, where
}m\in\mathbb{R}^{+}s.t.\forall PE_{i}^{k},b_{i}^{k}\geq 0,$ (16)
$\displaystyle
GEI=\frac{1}{\kappa}\sum_{k=1}^{\kappa}[\frac{1}{n\alpha(\alpha-1)}\sum_{i=1}^{n}[(\frac{b_{i}^{k}}{\bar{b^{k}}})^{\alpha}-1]].$
(17)

Specifically, a temporal GEI for each period is first calculated and then we
take the average of them across all periods. $\bar{b^{k}}$ is the mean of
$b_{i}^{k}$ in a given period $k$. $\alpha$ is a constant that regulates how
much attention is put on the larger percentage of errors, and here we set
$\alpha=2$.

####  4.2.2 Downstream Vehicle Rebalancing Evaluation

For the downstream performance evaluation of the vehicle rebalancing module,
we adopt the ride-hailing simulator utilized in Guo et al. [8]. For the
simulation and evaluation of various approaches, demand data from June 26,
2019, is employed. The simulator is configured with a fleet size of 2000
vehicles. With this setup, vehicle and demand locations are initialized. At
the start of the simulation, all vehicles are made available and evenly
distributed across the taxi zones.

Since demand origins and destinations are at the sub-regional level, random
road nodes within each sub-region are assigned as origins and destinations for
customers in that particular sub-region. The simulator comprises two
components: a matching engine, which is solved every 30 seconds, and a vehicle
rebalancing engine, which is solved every 300 seconds. In the vehicle
rebalancing model 10, the parameters are set as $\alpha=1$ and $\beta=10^{2}$.
The vehicle rebalancing problem takes into account $\kappa=6$ time intervals
ahead for optimization.

The simulation yields several key metrics for evaluating different rebalancing
models, including:

  1. 1.

Average customer wait time

  2. 2.

Standard deviation of customer wait time across zones

  3. 3.

Customer unsatisfaction rate

  4. 4.

Average non-occupied VMT

  5. 5.

Average number of rebalancing trips

These metrics are essential in assessing the performance and effectiveness of
various fairness-enhancing rebalancing approaches. The variation in customer
wait times, as measured by standard deviation, reflects the fairness of
services provided to customers. Meanwhile, other metrics are indicative of the
system’s overall efficiency.

###  4.3 Upstream Demand Prediction Results

In this section, we discuss the effect of the socio-demographically enriched
adjacency matrix on the performance of the upstream prediction of the ride-
hailing demand.

####  4.3.1 Performance Summary

In this section, we demonstrate the demand prediction performance of the SA-
STGCN model and different combinations of regularization terms compared to the
Historical Average model and the pure STGCN model as the baseline models.
Specifically, the Historical Average model is defined by using the historical
average of the demand on the same date of the week and time interval of the
day in the training set to predict the testing data.

Table 1 shows the prediction performance comparison among the two benchmark
models, the SA-STGCN model, and models with regularization terms implemented
in terms of accuracy and fairness. The first four metrics in the table (i.e.
MAE, RMSE, MAPE, and ME) demonstrate the accuracy performance of the models,
while the last two metrics (i.e. MVPE and GEI) illustrate the fairness
performance. The first section of the table 1 illustrates how SA-STGCN compare
with the baseline models, and the second, third, and fourth sections of table
1 refer to the performance of the models with regularization terms penalizing
overestimation, limiting error distribution, and the models with both
regularization terms with different weight parameters.

| MAE | RMSE | MAPE | ME | MVPE |  GEI $(10^{-4})$
---|---|---|---|---|---|---
Historical Average | 3.699 | 5.293 | 0.721 | -0.885 | 8.347 | 5.463
STGCN | 3.130 | 4.334 | 0.738 | -0.046 | 9.054 | 5.948
SA-STGCN | 3.128 | 4.352 | 0.693 | 0.204 | 8.002 | 5.230
SA-STGCN ($\boldsymbol{\gamma=0.01}$) | 3.109 | 4.318 | 0.713 | 0.118 | 8.624 | 5.657
SA-STGCN ($\boldsymbol{\gamma=0.03}$) | 3.113 | 4.350 | 0.659 | 0.463 | 7.426 | 4.846
SA-STGCN ($\boldsymbol{\gamma=0.05}$) | 3.138 | 4.396 | 0.606 | 0.733 | 6.170 | 4.003
SA-STGCN ($\boldsymbol{\gamma=0.07}$) | 3.173 | 4.458 | 0.577 | 0.988 | 5.637 | 3.648
SA-STGCN ($\boldsymbol{\gamma=0.09}$) | 3.216 | 4.522 | 0.549 | 1.206 | 5.045 | 3.257
SA-STGCN ($\boldsymbol{\lambda=0.5}$) | 3.152 | 4.360 | 0.744 | -0.057 | 9.004 | 5.917
SA-STGCN ($\boldsymbol{\lambda=1}$) | 3.159 | 4.376 | 0.760 | 0.064 | 9.183 | 6.038
SA-STGCN ($\boldsymbol{\lambda=3}$) | 3.197 | 4.415 | 0.728 | 0.108 | 8.143 | 5.320
SA-STGCN ($\boldsymbol{\lambda=5}$) | 3.255 | 4.481 | 0.739 | 0.240 | 7.973 | 5.198
SA-STGCN ($\boldsymbol{\lambda=0.5,\gamma=0.09}$) | 3.136 | 4.359 | 0.723 | 0.143 | 8.934 | 5.863
SA-STGCN ($\boldsymbol{\lambda=1,\gamma=0.07}$) | 3.228 | 4.489 | 0.548 | 0.974 | 4.751 | 3.060
SA-STGCN ($\boldsymbol{\lambda=3,\gamma=0.03}$) | 3.346 | 4.575 | 0.568 | 0.786 | 4.540 | 2.929
SA-STGCN ($\boldsymbol{\lambda=5,\gamma=0.07}$) | 3.548 | 4.850 | 0.510 | 1.486 | 3.324 | 2.132
Table 1: Model cross-comparison.

As shown in the first section of the table 1, it is evident that using the
socio-demographically enriched matrix helps to improve both the accuracy and
the fairness metrics compared the benchmarks. The SA-STGCN is able to reduce
both the MVPE and GEI by 11.6% and 12.1% while not harming the accuracy
metrics. It even slightly improved the MAE and the MAPE results.

By cross-comparing the evaluation metrics of the performance of different
regularization terms, the proposed regularization terms improve overall
fairness significantly while not sacrificing model accuracy too much. In fact,
the accuracy metrics in all three regularization models are improved in most
cases compared to benchmarks. With extremely large weight parameters such as
when $\lambda=5$ and $\gamma=0.07$, the fairness metrics MVPE and GEI can be
reduced by 63.3% and 64.2%, respectively, while the accuracy metrics such as
MAE only increased by 13.4% compared to the pure STGCN. Moreover, the positive
outcomes of the relative error metric ME show that adding the regularization
helps the prediction to shift from overestimation to underestimation. This
transformation, as we will later illustrate, contributes significantly to the
enhancement of vehicle re-balancing downstream. The model with overestimation
estimation performs the best as it improves both fairness and accuracy metrics
at the same time.

The second and third sections of the table 1 also serve as the sensitivity
analysis of the regularization weight’s effect on the model performances. In
the case of overestimation penalization, there is a consistent accuracy-
fairness trade-off pattern, as the weight of regularization increases, the
error magnitudes monotonically increase, the percentage error decreases, and
the fairness improves. On the other hand, when restricting the error
distribution, as we increase the magnitude of the weight of the regularization
term, only the MAE, RMSE, and ME monotonically increase, but the MAPE and the
two fairness metrics first increase then decrease.

####  4.3.2 Fairer Prediction in Space

(a) MAE spatial distribution

(b) MAPE spatial distribution

(c) ME spatial distribution

Figure 5: Error spatial distribution in Manhattan.

Figure 5 demonstrates the spatial distribution of the error metrics across the
study area of the pure STGCN, SA-STGCN, and the selected models with
regularization terms. In general, the prediction errors are larger in
magnitude in the downtown regions, while the percentage errors have more
variation in the regions with low demand, such as the northern tip of the
island. When comparing various models, the MAE plots reveal similar
distributions, indicating that the prediction performances are not highly
sensitive to the proposed changes in the model. In contrast, the MAPE plots
demonstrate that models incorporating regularization terms exhibit a more
uniform error distribution across space, reflecting a fairer prediction. The
ME distributions suggested the general error direction shifted from negative
to positive as regularization terms are introduced, which means a transition
from overestimation to underestimation. We later demonstrate that this shift
could be beneficial for promoting fairness in downstream vehicle rebalancing
operations.

####  4.3.3 Fairer Prediction in Time

(a) MAE temporal distribution

(b) MAPE temporal distribution

(c) ME temporal distribution

(d) MVPE temporal distribution

Figure 6: Error temporal distribution across times of the day.

Figure 6 illustrates the temporal distribution of the error metrics across the
time of the day. In general, the error magnitude and percentage distribution
pattern follow the demand level, with smaller MAE values and larger MAPE and
MVPE when demand is low and vice versa. In contrast, the error direction
displays a less regular pattern. Compared to the benchmark performance of the
pure STGCN model, the proposed SA-STGCN model and the method of adding
regularization terms can reduce the peak errors in all scenarios.
Specifically, SA-STGCN adding both regularization terms has the most direct
impact on smoothing the MAE, MAPE, and MVPE temporal distribution. The
smoothing effect is most significant in the early morning time when error
values are more extreme. In addition, regularization terms have various
effects on the error directions across time. When we add both regularization
terms, the ME distribution shifts to positive the most as shown by the purple
line. On the other hand, adding the error restriction regularization term has
the least effect on day-time ME distribution. The temporal trend of RMSE is
similar to MAE and the GEI trend is similar to that of MVPE, so the figures
didn’t include these two metrics.

###  4.4 Downstream Vehicle Rebalancing Performances

In this section, we discuss the effectiveness of our models when applied to
vehicle reallocation tasks, utilizing a simulator based on real-world ride-
hailing data.

####  4.4.1 Performance Summary

| Unsatisfaction | Wait Time | Wait Time | Non-occupied | Rebalancing Trip
---|---|---|---|---|---
| Rate (%) | Avg (seconds) | Std (seconds) | VMT (miles) | Number
True Demand | 1.76 | 89.65 | 22.07 | 60.82 | 20.03
Historical Demand | 1.75 | 90.55 | 22.76 | 60.81 | 19.47
Baseline STGCN | 1.79 | 89.83 | 22.52 | 60.34 | 19.40
Baseline SA-STGCN | 1.74 | 89.75 | 22.13 | 60.20 | 19.25
SA-STGCN ($\boldsymbol{\gamma=0.01}$) | 1.77 | 89.88 | 22.08 | 60.49 | 19.50
SA-STGCN ($\boldsymbol{\gamma=0.03}$) | 1.76 | 89.95 | 22.53 | 60.29 | 19.25
SA-STGCN ($\boldsymbol{\gamma=0.05}$) | 1.76 | 89.51 | 21.72 | 60.21 | 19.36
SA-STGCN ($\boldsymbol{\gamma=0.07}$) | 1.72 | 89.67 | 21.77 | 60.00 | 19.08
SA-STGCN ($\boldsymbol{\gamma=0.09}$) | 1.73 | 89.58 | 21.78 | 60.00 | 19.15
SA-STGCN ($\boldsymbol{\lambda=0.5}$) | 1.73 | 90.16 | 22.34 | 60.37 | 19.28
SA-STGCN ($\boldsymbol{\lambda=1}$) | 1.77 | 90.03 | 22.17 | 60.34 | 19.28
SA-STGCN ($\boldsymbol{\lambda=3}$) | 1.78 | 89.98 | 22.15 | 60.36 | 19.33
SA-STGCN ($\boldsymbol{\lambda=5}$) | 1.82 | 89.99 | 21.75 | 60.15 | 19.14
SA-STGCN ($\boldsymbol{\lambda=0.5,\gamma=0.09}$) | 1.75 | 89.39 | 21.06 | 59.87 | 19.09
SA-STGCN ($\boldsymbol{\lambda=1,\gamma=0.07}$) | 1.77 | 89.70 | 21.72 | 60.04 | 19.17
SA-STGCN ($\boldsymbol{\lambda=3,\gamma=0.03}$) | 1.73 | 90.02 | 22.10 | 59.99 | 18.90
SA-STGCN ($\boldsymbol{\lambda=5,\gamma=0.07}$) | 1.74 | 90.44 | 20.62 | 60.11 | 18.70

Table 2: Model performance summary.

Table 2 presents a summary of how various demand models perform in addressing
the vehicle rebalancing problem, specifically when employing the fairness-
focused MIVR model. This evaluation includes scenarios where true demand is
known and those relying solely on average historical demand for future
predictions, serving as benchmark models. Additionally, a standard STGCN and a
baseline SA-STGCN model without additional regularization terms are also
employed for benchmarking purposes.

Moreover, the evaluation also encompasses three variations of the SA-STGCN
model: (i) SA-STGCN with a focus on penalizing overestimation, (ii) SA-STGCN
with limited error distribution, and (iii) SA-STGCN incorporating both
regularizations. Crucial customer service metrics assessed include the rate of
customer dissatisfaction, average waiting times, and the variability of these
waiting times across different sub-regions. To demonstrate the effectiveness
of the vehicle rebalancing algorithms in enhancing operational efficiency, we
examine metrics like the average Vehicle Miles Traveled without passengers per
vehicle and the average number of rebalancing trips each vehicle undertakes.

####  4.4.2 Fair Prediction Leads to Fair Service

The first significant insight from the simulation results is the superior
performance of predictions that incorporate fairness considerations, compared
to benchmark prediction models. These enhanced models excel in two main
aspects: reducing average customer wait times and achieving a more consistent
wait time across different sub-regions. This improvement suggests that
factoring in fairness can lead to more efficient and equitable service
outcomes.

Further analysis reveals that the SA-STGCN model, when compared to the
baseline STGCN, is more effective in satisfying a larger number of customers
while simultaneously reducing the average wait time. Notably, this model also
succeeds in minimizing the variance in service provision across different
regions, addressing the issue of regional disparities in service quality.

The benefits of the SA-STGCN model stem from two primary factors. Firstly, it
outperforms the traditional STGCN model in terms of both prediction accuracy
and fairness indicators. These enhanced performances translate into more
effective rebalancing operations, ensuring a fairer distribution of services
with less disparity in error rates across regions. Secondly, the integration
of socio-demographic information within the STGCN framework leads to a more
conservative approach in demand estimation. This conservatism, while
acknowledging the inherent inaccuracies in demand prediction, results in fewer
non-occupied VMT and a reduced number of rebalancing trips. Consequently, this
conservative approach benefits the overall system operation.

Moreover, the incorporation of additional regularization terms in the SA-STGCN
models could potentially enhance model performance further. This improvement
would be due to the reasons discussed above, emphasizing that fairer
predictions not only improve service efficiency but also contribute to
equitable service distribution. Ultimately, the proposed fairness-enhancing
vehicle rebalancing approach fosters a win-win scenario, enhancing both the
efficiency and fairness of ride-hailing services.

####  4.4.3 The Power of Demand Underestimation

The second major insight from the simulation results highlights the
significant role of demand underestimation in ride-hailing rebalancing
operations. This underestimation, prompted by the addition of a penalization
term (associated with the parameter $\gamma$) to errors in demand
overestimation, results in more equitable predictions. Despite a decrease in
prediction accuracy, this approach leads to improved service provision for
customers and reduces disparities in services across regions.

The advantage of demand underestimation lies in its inherent conservativeness.
As Guo et al. [8] suggest, in scenarios where future demand is uncertain,
adopting a less aggressive approach often yields better outcomes. This
conservatism allows for a more efficient distribution of limited vehicle
resources, particularly important given the high costs associated with
incorrect rebalancing decisions.

However, excessively penalizing demand overestimation in ride-hailing
operations is not ideal. The simulation indicates that the optimal balance is
achieved when $\gamma$ is set to 0.05. This parameter setting results in the
best average customer wait times and the fairest service distribution across
different regions. It’s important to note that while increasing $\gamma$ does
lead to fairer predictions, the impact on downstream services is not
monotonic. Excessive conservatism in vehicle rebalancing can be
counterproductive. Therefore, identifying an appropriate level of
conservativeness is crucial for making optimal rebalancing decisions.

####  4.4.4 The Most Fair Model

In the comparative analysis of models presented in Table 2, the SA-STGCN model
with $\lambda=5$ and $\gamma=0.07$ emerges as the most equitable in terms of
service provision to customers. This model significantly reduces the
variability in customer wait times by 8.43% compared to the baseline STGCN
model, albeit at a slight increase in average wait times of 0.68%. Notably,
this model also excels in fairness regarding demand prediction, achieving the
lowest MVPE of 3.32 and GEI of 2.13. These results underscore the correlation
between fairer prediction models and more equitable service provision in the
downstream.

Conversely, when considering a balance between efficiency and fairness in
vehicle rebalancing, the SA-STGCN model with $\lambda=0.5$ and $\gamma=0.09$
stands out. In comparison to the baseline STGCN model, it successfully lowers
both the standard deviation and average of customer wait times by 6.48% and
0.49%, respectively. Impressively, this model even outperforms scenarios with
perfect demand knowledge in terms of average customer wait times. This can be
attributed to the fairness-enhancing MIVR model, which approximates the
matching component to account for future time intervals. Such approximations,
while not perfectly optimal for real-world ride-hailing scenarios, demonstrate
that sometimes, less accurate demand predictions can paradoxically lead to
more efficient system operation.

####  4.4.5 Trade-offs of Introducing Fairness Weights

| Unsatisfaction | Wait Time | Wait Time | Non-occupied | Rebalancing Trip
---|---|---|---|---|---
| Rate (%) | Avg (seconds) | Std (seconds) | VMT (miles) | Number
True Demand | 1.81 | 89.49 | 22.55 | 60.70 | 20.13
Historical Demand | 1.78 | 90.51 | 22.62 | 60.73 | 19.53
Baseline STGCN | 1.79 | 89.79 | 22.80 | 60.36 | 19.50
Baseline SA-STGCN | 1.75 | 89.74 | 22.69 | 60.15 | 19.23
SA-STGCN ($\boldsymbol{\gamma=0.01}$) | 1.79 | 89.87 | 22.78 | 60.29 | 19.38
SA-STGCN ($\boldsymbol{\gamma=0.03}$) | 1.77 | 90.11 | 22.58 | 60.29 | 19.21
SA-STGCN ($\boldsymbol{\gamma=0.05}$) | 1.75 | 89.57 | 22.28 | 60.04 | 19.25
SA-STGCN ($\boldsymbol{\gamma=0.07}$) | 1.73 | 89.50 | 22.21 | 59.82 | 19.02
SA-STGCN ($\boldsymbol{\gamma=0.09}$) | 1.76 | 89.32 | 22.56 | 59.88 | 19.16
SA-STGCN ($\boldsymbol{\lambda=0.5}$) | 1.79 | 89.77 | 22.37 | 60.17 | 19.30
SA-STGCN ($\boldsymbol{\lambda=1}$) | 1.76 | 90.14 | 22.59 | 60.21 | 19.13
SA-STGCN ($\boldsymbol{\lambda=3}$) | 1.78 | 90.02 | 23.01 | 60.07 | 19.10
SA-STGCN ($\boldsymbol{\lambda=5}$) | 1.77 | 89.80 | 22.50 | 60.03 | 19.14
SA-STGCN ($\boldsymbol{\lambda=0.5,\gamma=0.09}$) | 1.74 | 89.21 | 21.84 | 59.89 | 19.24
SA-STGCN ($\boldsymbol{\lambda=1,\gamma=0.07}$) | 1.80 | 89.70 | 21.96 | 59.83 | 19.05
SA-STGCN ($\boldsymbol{\lambda=3,\gamma=0.03}$) | 1.78 | 90.03 | 22.35 | 60.03 | 18.99
SA-STGCN ($\boldsymbol{\lambda=5,\gamma=0.07}$) | 1.75 | 90.35 | 21.79 | 59.91 | 18.63

Table 3: Model performance summary without considering fairness weights in the
MIVR model.

Finally, we explore the implications of incorporating fairness weights into
the MIVR model. Table 3 presents the performance metrics of the MIVR model
sans the application of fairness weights in determining vehicle rebalancing
strategies.

When analyzing the results from both tables, two significant insights are
drawn. First, incorporating fairness weights into the MIVR model notably
improves fairness, especially by diminishing discrepancies in customer wait
times. Additionally, this approach results in serving a higher proportion of
customers. This improvement is attributed to better servicing of customers in
previously underserved areas, as more vehicles are strategically repositioned
there. Evidence of this is seen in the increased average distance traveled by
non-occupied vehicles (VMT) and the reduced number of rebalancing trips, which
supports our hypothesis. However, the second observation reveals a compromise:
while fairness is enhanced, there is an observable rise in the average
customer wait time across the system.

##  5 Policy Discussion

On October 30, 2023, President Joe Biden issued an executive order focusing on
“safe, secure, and trustworthy artificial intelligence” [80], emphasizing the
critical need to address the risks associated with artificial intelligence and
establish new standards for its safety and security. This study reveals
fairness issues within ride-hailing service algorithms, prompting
consideration for regulatory interventions that would compel ride-hailing
companies to integrate fairness considerations into their algorithmic design.
For instance, governments can mandate that the variation in wait times across
neighborhoods should not exceed a predefined threshold. Governments may also
prescribe specific weights $\omega_{i}$ for individual regions within the
vehicle rebalancing objective function (Equation 10), thereby exerting control
over the importance assigned to successful matching in each distinct region
$i$.

Concerning ride-hailing companies, the fairness-enhancing algorithm introduced
in this research offers an effective solution to improve fairness in ride-
hailing service provision. By adopting the proposed fairness-enhancing
strategies in both demand prediction and service rebalancing, ride-hailing
companies can greatly reduce variations in passenger wait times across the
region. It’s worth highlighting that with the proper selection of
hyperparameters $\lambda$ and $\gamma$ in the objective function of demand
prediction (Equation 3.1.2), both the variation and average customer wait time
can be reduced. This achievement positions ride-hailing service companies to
attain a Pareto improvement, concurrently enhancing both efficiency and
fairness in their operations and achieving a “win-win” scenario.

To enhance equity in vehicle distribution, ride-hailing services can adopt
strategies like Lyft’s ’Power Zones.’ These zones, located in underserved
areas, offer drivers bonuses for accepting rides originating from these
regions. This approach addresses the income disparity caused by low-demand
zones, where surge pricing is less frequent and earning opportunities are
diminished. By incentivizing drivers to operate in these areas, companies can
not only ensure better service coverage but also support drivers in
maintaining consistent earnings.

From the perspective of passengers, this approach, which aims for a more
equitable distribution of wait times among communities, especially benefits
individuals facing challenges with transportation options. By fine-tuning both
demand and rebalancing models, it has the potential to simultaneously attain a
lower and more equitable wait time distribution among people from different
communities. This improvement enhances mobility and connectivity across all
communities, fostering trust among passengers in the ride-hailing service,
especially within disadvantaged communities.

The ride-hailing service plays a pivotal role as a transportation solution for
individuals seeking employment and opportunities. The decrease in wait times
translates to more efficient access to opportunities for residents in diverse
communities, offering significant relevance for areas with elevated
unemployment rates or limited local job options. Through the adoption of this
fairness-enhancing algorithm, ride-hailing companies not only showcase their
commitment to social responsibility but also actively contribute to the
overall well-being and inclusivity of the communities they serve.

##  6 Conclusion

This study presents a pioneering framework aimed at enhancing fairness in both
predicting ride-hailing demand and delivering equitable service to riders. The
framework introduces a Socio-Aware Spatio-Temporal Graph Convolutional Network
(SA-STGCN), which integrates a socio-enriched adjacency matrix and bias-
reduction regularization methods. Additionally, it features a vehicle
rebalancing engine that incorporates fairness considerations into its
objective function. This framework was evaluated using a simulator with real-
world ride-hailing data, demonstrating that the SA-STGCN model not only
outperforms standard demand prediction models in accuracy but also in
fairness. Significantly, improvements in fairness at the demand prediction
stage lead to more equitable service delivery in the vehicle rebalancing
process. The vehicle rebalancing module, enhanced with fairness weights,
showed a notable reduction in both the standard deviation and average of
customer wait times by 6.48% and 0.49%, respectively, suggesting a win-win
scenario where both efficiency and fairness are improved for ride-hailing
platforms.

The proposed framework offers a viable approach for ride-hailing companies to
integrate fairness into their operations, and it provides a basis for
government regulations aimed at preventing service imbalances across different
areas. However, realizing the win-win scenario highlighted in the study
involves addressing practical challenges. A key solution lies in developing
driver incentive mechanisms. These mechanisms should ensure that drivers are
motivated to serve in underserved communities and that their earnings remain
stable despite such commitments. As the role of ride-hailing services becomes
more central in our everyday activities, it’s crucial to make certain that
these platforms maintain a strong commitment to social responsibility and
proactively enhance the well-being and inclusiveness of the communities they
operate in.

For future research, it would be beneficial to include a focus on driver
behaviors and earnings, which this study has not addressed. A comprehensive
framework could be developed to enhance fairness across all aspects of the
ride-hailing vehicle rebalancing operations: demand prediction, fairness for
riders, and fairness for drivers. Such a framework should ensure that drivers
who are redirected to serve underserved communities are compensated equitably,
comparable to those serving in city centers. This approach would create a more
balanced and fair environment for all parties involved in the ride-hailing
ecosystem.

## Acknowledgements

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