# Ride-hailing Vehicle Rebalancing Strategies Under Disruptions: A Case Study in Athens

Euntak Lee, Rim Slama, Nikolas Geroliminis, Ludovic Leclercq

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Euntak Lee, Rim Slama, Nikolas Geroliminis, Ludovic Leclercq. Ride-hailing Vehicle Rebalancing Strategies Under Disruptions: A Case Study in Athens. 9th International IEEE Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS), Sep 2025, Luxembourg, Luxembourg. hal-05263312

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# Ride-hailing Vehicle Rebalancing Strategies Under Disruptions: A Case Study in Athens

Euntak Lee

ENTPE, LICIT-ECO7

Univ. Eiffel

Lyon, France

euntak.lee@univ-eiffel.fr

Rim Slama

ENTPE, LICIT-ECO7

Univ. Eiffel

Lyon, France

rim.slamasalmi@entpe.fr

Nikolas Geroliminis

Urban Transport Systems Laboratory (LUTS)

Ecole Polytechnique Federale de Lausanne (EPFL)

1015 Lausanne, Switzerland &

MobiLysis (MOBL)

Chemin De La Raye 13, 1024 Ecublens, Switzerland

nikolas.geroliminis@epfl.ch

Ludovic Leclercq

ENTPE, LICIT-ECO7

Univ. Eiffel

Lyon, France

ludovic.leclercq@univ-eiffel.fr

**Abstract**—The global ride-hailing (RH) industry plays an essential role in multi-modal transportation systems by improving user mobility, particularly as first- and last-mile solutions. While many RH rebalancing studies focus on nominal scenarios with regular demand patterns, it is crucial to consider disruptions that negatively impact operational efficiency. This study examines how RH rebalancing strategies can strengthen the resilience of multi-modal transportation systems against supply-side disruptions. We incorporate RH services into systems where users choose and switch transportation modes based on their preferences, accounting for uncertainties in demand predictions. To address the stochastic supply-demand dynamics, we propose a multi-agent reinforcement learning (MARL) strategy, specifically utilizing a multi-agent deep deterministic policy gradient (MADDPG) approach. The results demonstrate significant improvements in key performance indicators, including user waiting time, resilience metrics, total travel time, and travel distance.

**Index Terms**—Ride-hailing services, Rebalancing strategy, Resilience, Multi-modal transportation systems, Reinforcement learning

## I. INTRODUCTION

Ride-hailing (RH) mobility services are expected to transform the future of multi-modal transportation systems. RH services account for about 10% of all trips in large cities, and users are expected to have the potential to reduce their dependence on private cars [1]. The role of RH services in first and last mile connectivity is essential to encourage the shift from private cars to public transportation-based multi-modal trips [2]. Furthermore, a greater use of RH services is associated with a greater frequency of public transportation systems, such as metros, buses, and trains [3], [4].

Yet, alongside these opportunities lies a pressing challenge: the disruptions that frequently compromise the performance and reliability of such interconnected networks. Disruptions in multi-modal transportation networks, whether stemming from supply or demand-side issues, pose a significant threat to system performance and user satisfaction.

Supply disruptions lead to reduced availability of the road network, which can occur due to road accidents or lack of mobility services. On the other hand, demand disruptions with excessive demand can result in interruptions in system functioning due to limited supply capacity. As a cascading effect, these types of disruptions could cause all users to experience longer travel times, higher costs, increased transfers, and more service delays [5], [6].

As part of the multi-modal transportation systems, appropriate RH service operations can provide a promising way to improve resilience. A more resilient system must be established for operational efficiency that can withstand and absorb the negative impacts of disruptions, maintain a certain level of service, and recover quickly [7]. Strengthening interrelationships among transportation modes is one of the key solutions to resist against increasing burden of other transportation modes during disruptions.

### A. Resilience Assessment of Transportation Systems

The concept of resilience has been focused on measuring the practical performance of systems in different phases of disruption. For example, Jenelius and Cats [8] measured the robustness and redundancy of a public transport system when disruptions occur such as service rate reductions and link breakdowns. They proposed the measurements by applying the passenger welfare, or total utility, of a generalized cost function that includes in-vehicle time, waiting time, walking time, and number of transfers. Xu et al. [9] proposed a tolerance function that expects worst-case scenarios to evaluate a system's performance under rail transit disruptions. By applying the function, they suggested the optimal disruption mitigation strategy, such as platform downtime protection and bus-bridging service planning. Similarly, various metrics for different concepts have been proposed, including recovery cost [10], centrality [11], minimum system performance
[12], readiness [13], route diversity [14], and rapidity [15]. However, most of the existing metrics are associated with any of the following limitations: (i) resilience from either but not both perspectives of network structure or passenger demand is considered; (ii) static attributes of systems are mainly considered, neglecting dynamic features such as real-time flows of passengers and vehicles; or (iii) impractical assumptions are applied as responses to disruptions are not considered. To overcome this, [16] recently proposed a combination of resilience metrics in four aspects: vulnerability, adaptability, robustness, and recoverability. These metrics consider the impacts of disruptions on passenger choices of paths and a dynamic simulation procedure in the overall disruption phases. Multifaceted evaluation can provide insights into how the system should be assessed, which reactions should be needed to handle disruptions, and how to improve resilience.

Nevertheless, the resilience of RH services within multi-modal transportation systems remains unexamined. The RH studies primarily focused on improving the operational efficiency of RH services under regular scenarios with consistent demand patterns [17], [18], [19]. For reliable operations, it is essential to explore how RH services contribute to the resilience of multi-modal transportation systems against disruptions. This study seeks to bridge this gap by studying resilience assessment while integrating RH services within multi-modal transportation systems to enhance system robustness and adaptability to disruptions.

## B. Ride-hailing Rebalancing Strategies

RH services offer the convenience of allowing users to request rides to any location of their choice. Leveraging these strengths, RH companies such as Uber, Lyft, and Bolt have transformed urban mobility by providing flexible, on-demand transportation options. However, this freedom may cause supply-demand imbalances in local areas. Users cannot request rides if there are no RH vehicles nearby, while other areas are oversupplied with vehicles. Consequently, vehicle fleet management has gained interest for efficient operations. However, operating an appropriate strategy is not a simple issue since inefficient operations can instead lead to longer vacant times and longer waiting times for drivers and passengers, respectively [20]. Moreover, as extra RH vehicles cannot be deployed whenever there is a shortage, managing this imbalance is one of the critical issues [21].

To improve the reliability of RH service operations, centralized and decentralized systems have been proposed for rebalancing RH vehicles, as shown in Fig. 1. In a centralized system, a single main operator manages the entire network with the objective of maximizing overall RH service performance. In contrast, a decentralized system involves multiple local operators, each focused on optimizing the performance of their respective areas independently.

1) Centralized Strategies: Centralized RH rebalancing strategies have been studied mainly from a driver perspective. For example, [22] and [23] suggested dynamic surge pricing strategies that led drivers to decide their relocating area in

the next assignment to maximize their profits. They showed improvements in service quality by reducing user waiting times and increasing driver revenue. However, this approach had limitations that certain low-demand areas were not covered due to the indirectness of encouraging drivers to move, which consequently led users in the areas to change their travel options to a more reliable transportation mode. To overcome this issue, many studies have explored the driver decision-making processes when searching for the next passengers. The proposed strategies include minimizing the relocating distance [24] and the waiting time [25], and maximizing the potential revenue of a driver [26] and the probability of matching [27].

2) Decentralized Strategies: In parallel, decentralized RH rebalancing strategies have been steadily studied, leveraging their ability to scale to large-scale scenarios that involve extensive fleet sizes, a substantial number of ride requests, and complex road networks. In these approaches, individual vehicle entities maximize their objectives based on distributed methods in order to convert a main fleet rebalancing problem into several subproblems that are computationally less expensive. For instance, [28] utilized a probabilistic decision approach to optimize each vehicle path to balance supply-demand while minimizing expected cost. [29] utilized a gravitational algorithm that allows each vehicle to find its relocation area to maximize its own self-interest using incomplete historical information. [30] proposed a region partitioning method for vehicle relocation considering historical information of spatial and temporal ride requests, showing high-performance results even when the fleet size reaches 10,000. [31] utilized a discrete probability approach with each vehicle operating independently, based on historical data for pick-up and drop-off. They found that not sharing information with others can lead difficulties in managing local supply-demand imbalances.

3) Reinfocement Learning-based Strategies: In recent years, reinforcement learning (RL) has been applied as an effective method in optimizing vehicle agents’ decision-making policies. In a dynamic environment where agents do not obtain global observations, RL algorithms such as Q-learning, Deep Q-Network, and temporal difference learning have been employed [32]. Thereafter, multi-agent reinforcement learning (MARL) has been introduced focusing on agent communication and coordination [33], [34], [35], [36].

While most MARL-based studies have enhanced the operational performance of RH systems, they mainly focused on

<figure><img src="image_2.png" /><figcaption>Fig. 1. Comparison of centralized and decentralized systems.</figcaption></figure>
the movements of vehicles themselves, neglecting interconnections with other transportation modes. To effectively integrate RH services into the systems, it is essential to consider both traffic dynamics and user travel behaviors. Moreover, they assumed that relocations are completed within a single time step and the relocated ones were immediately matched with users. In reality, however, it requires some time steps for relocations and vehicles can be matched while relocating.

### C. Objective of the Study

From the above discussion, three key research gaps can be summarized as follows.

* First, most previous studies have not considered the aspect of multi-modality for users. Although multiple transportation modes interacted in the road networks, users were unable to switch modes once they departed on their trips. Limited attention has been given to scenarios where users transfer between different modes or adjust their travel plans in response to unexpected changes.

* Second, the impacts of RH rebalancing strategies on the systems have been studied in regular scenarios. As the worldwide RH industry grows, further studies regarding resilience with the integration of multi-modal transportation systems need to be assessed across various disruption scenarios.

* Third, most studies have applied historical pick-up and drop-off data. However, uncertainty in spatial-temporal future ride requests must be considered to effectively address local supply-demand imbalances with proactive rebalancing strategies. In particular, disruptions provide further discrepancies between prediction and reality.

To bridge these research gaps, the resilience of RH rebalancing strategies in the multi-modal transportation systems during supply disruptions is assessed in this study. A MARL-based RH rebalancing framework, augmented with deep learning capabilities, has been proposed and developed to minimize matching time. RH vehicles, acting as agents, utilize a centralized training and decentralized execution framework, effectively enhancing system performance while reducing computational burden. Moreover, the RH systems are considered to operate under uncertainties, including demand prediction noise and delay in response to disruptions. A traffic simulation model is implemented using a trip-based MFD model that includes multiple transportation modes such as trains, metros, buses, RH vehicles, and background traffic. Users are set to opt for various transportation options that best fit their preferences and can also change their choices at any time if the situation changes from what they have expected. With disruption scenarios on train lines, the system performance is evaluated with resilience metrics using average travel time and transfer waiting time.

## II. METHODOLOGY

### A. Multimodal Transportation Systems

1) Road Network: A road network with a large service area is designed as the basic structure, as shown in Fig. 2.

The transportation modes include metros, trains, buses, RH vehicles and other vehicles. These modes are connected across different network layers by nodes, enabling users to transfer between them for multi-modal trips.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Illustration of individual layers in a multi-modal transportation network, and their integration into a comprehensive road network.</figcaption></figure>

All vehicles on the network are assigned the same speed at a given time step if they are in the same region and operate the same mode, following the multi-modal macroscopic fundamental diagram (MFD) principle [37].

In bus and car systems, a trip-based MFD model is employed as they interact on the road. In general, travel time of vehicle i of type m, denoted as $T_i^m$, is associated with the travel distance $l_i^m$, departure time $t_i$, and the speed $v_m^r(t)$ at time t in region r, and it can be mathematically expressed as follows:

$$l_i^m = \int_{t_i}^{t_i + T_i^m} v_m^r(t) dt. \quad (1)$$

In the MFD framework, it is assumed that the speed of a transportation mode $v_m^r(t)$ is the same for all users in the same region sharing the same mode at the same time [38]. This speed corresponds to the multi-modal MFD curves, which usually depend on the accumulation number of all transportation modes on the road in the region. The speed formula for buses, private cars, and RH vehicles is defined as follows:

$$v_m^r(t) = V_m^r(\{n_{m'}^r(t), \forall m' \in \mathcal{M}\}) \quad (2)$$

where, $n_{m'}^r(t)$ denotes the number of vehicles of type m' in service area r at time t. $\mathcal{M}$ represents all vehicle types considered in the simulation. $\{n_{m'}^r(t), \forall m' \in \mathcal{M}\} \rightarrow \{V_m^r, \forall m' \in \mathcal{M}\}$ describes the multi-modal MFD speed function, which captures the congestion dynamics and interactions between modes in service area r at time t. The speed is assumed to be always greater than zero to avoid a complete gridlock. Therefore, the relationship for cars and buses can be formulated as follows using Equation 1:

$$l_i^{m'} = \int_{t_i}^{t_i + T_i^{m'}} V_m^r(\{n_{m'}^r(t), \forall m' \in \mathcal{M}\}) dt. \quad (3)$$

Here, RH vehicles can freely cross the road without any lines. They are operated by transitioning vehicle states between Idle, Relocating, Pick-up, and Serving. Meanwhile, since metros and trains are unaffected by traffic conditions, their average speeds are set at 13 m/s and 30 m/s, respectively.
2) User Trips: Given user OD distribution, departing users select their travel paths in two steps. Firstly, at most five candidate shortest paths are searched using the Dijkstra method. Considering total travel time as a cost, users also consider possible external delays such as walking time, transfer waiting time, and service rate. The candidate paths have different combinations of transportation modes, but parts of them can be the same. Secondly, one candidate is selected as a user path by employing a logit model that describes the user's travel behavior. The utility function, its component, and the probability function of path choice are formulated as follows:

$$U_i = V_i + \epsilon_i \quad (4)$$

$$V_i = \sum_{q_i} \frac{d_t(q_i)}{v_t} + \sum_{p_i} \frac{d_m(p_i)}{v_m} + \sum_{l_i} \frac{d_b(l_i)}{v_b(l_i)} + \sum_{s_i} \frac{d_r(s_i)}{v_r(s_i)} \quad (5)$$

$$P_i = \frac{e^{-\theta \times U_i}}{\sum_i e^{-\theta \times U_i}} \quad (6)$$

where, Equation 4 represents the random utility of path i, $U_i$, consisting of the deterministic component $V_i$ and the unobservable error $\epsilon_i$. Here, it is assumed that the error term follows a Gumbel distribution. The deterministic component $V_i$ in Equation 5 is calculated as the total sum of travel times for each transportation mode. Travel times for regions q, p, l, and s are determined by multiplying the travel speeds $v_t$, $v_m$, $v_b(l_i)$, and $v_r(s_i)$ by the travel lengths $d_t(q_i)$, $d_m(p_i)$, $d_b(l_i)$, and $d_r(s_i)$ for trains, metros, buses, and cars, respectively. $P_i$ in Equation 6 represents the probability that a user will choose the path i.

## B. RH Operations

The RH systems are assumed to include two subjects: drivers and operators. They interact each other while having different objectives. Here, the driver's utility is the expected revenue from serving passengers. Drivers of vacant vehicles receive relocation offers from operators to move to depots. Drivers accept or refuse these offers based on their utility function.

1) Demand Prediction: Meanwhile, the RH system operator aims to ensure a sufficient number of vehicles are available to meet the expected demand. Operators cannot deploy additional vehicles whenever there is a shortage. Therefore, it is critical for the system to operate and handle local supply-demand imbalances within the limited number of vehicles. Considering the discrepancies between predicted and actual demand, it is inefficient to always relocate the vehicles to the same number as the predicted demand. When demand becomes higher, the probability that all predicted users actually request is exponentially low. To estimate the probability of matching, a survival function is adapted from [39], as shown

in Equations 7 and 8.

$$P(\hat{k}) = \frac{1}{2} \left( 1 - \frac{2}{\sqrt{\pi}} \int_{0}^{\frac{\hat{k}-\mu}{\sigma\sqrt{2}}} e^{-u^2} du \right) \quad (7)$$

$$\hat{k} = k + \epsilon(k, p), \quad \epsilon(k, p) \sim N\left(0, \sqrt{\frac{\pi}{2}}pk\right) \quad (8)$$

where, Equation 7 represents the probability of the survival function $P(\hat{k})$ that the predicted $\hat{k}$ users all request RH vehicles. It is defined as the complement of the cumulative distribution function of the normal distribution with a mean $\mu$ and a standard deviation $\sigma$ of user demand. Equation 8 represents the number of predicted users obtained by adding 10% of departing users in the next five minutes, k, with a noise $\epsilon(k, p)$ where p is the average relative noise. This noise, or uncertainty, in the demand prediction values can even worsen the discrepancies.

This survival function helps estimate the probability of a completion of the matching for those relocated. If the probability is below a certain threshold level, it would not be appropriate to publish that amount of relocation offers since the actual number of ride requests might not occur as expected. In this study, the threshold probability is set as 0.2, which is correspondingly paired with the upper bound in the number of relocation offers, $k_{max}$. In other words, the operators can publish $k_{max}$ offers at maximum. As a consequence, the number of relocation offers, d, is determined to be $\hat{k}$ or $k_{max}$ using Equation 9.

$$d = \arg\max_{x \in \{\hat{k}, k_{max}\}} P(x) \quad (9)$$

However, if disruptions occur, the number of relocation offers may exceed the upper bound to handle a surge in demand in specific areas. Specifically, the estimated number of users stranded on the affected lines is considered for relocation offers.

2) MARL-based RH rebalancing strategy: In the simulation environment, the agents observe their states in global and local information. Based on their state, they execute actions and obtain rewards for the actions. The MARL algorithm utilizes the action, state, and reward information to update the decision-making policy. The objective of the policy is to minimize the average vacant time of the agents. A detailed explanation of agent, state, action, and reward is as follows.

**Agent.** Each agent is set as a vacant RH vehicle. They decide whether to remain Idle or relocate to depots for the next match.

**State.** Each agent observes its environment state only when it is Idle. The environment state, represented as $x = [x_g, x_l]$, consists of global and local information.

The global information ($x_g = [g_d, n_d^{RH}, n_d^{PT}, b_d]$) includes multiple factors that provide a comprehensive view of the system's supply-demand dynamics: (i) Expected revenue distribution for relocation to depots ($g_d$); (ii) Distribution of vehicles already relocated to depots ($n_d^{RH}$); (iii) Availability of alternative transportation modes near depots ($n_d^{PT}$); and (iv) Supply-demand gap distribution at each depot ($b_d$).
The local information ($x_l = [n_v]$) includes the number of Idle vehicles within a 500 m distance. Since they are under similar circumstances, this observation promotes cooperative environments with information to recognize each other, which prevents over-supply when relocated to the same depot [34].

**Action.** Upon the given state, only Idle agents are assigned to take actions for selecting depots for relocation. The set of possible actions for relocation is defined as $a = [p_0, p_1, p_2, ..., p_k]$, where $[p_1, p_2, ..., p_k]$ represents the k possible depots for relocation, and $[p_0]$ represents the option to cruise without selecting any depot. The action space is set to be continuous to utilize the deterministic gradient framework.

**Reward.** In this study, the duration of vacant time following an agent's action is set as reward. A higher positive reward is granted for quicker matches within a specified time threshold. Conversely, a greater negative penalty is applied as vacant time exceeds the threshold. A reward function for agent i, $r^i$ is defined in Equation 10 as follows:

$$r^i = 20 \times \left( 2 \times \frac{1}{1 + e^{0.3 \times (t_i - t_h)}} - 1 \right) \quad (10)$$

Where, $t_i$ is the duration that agent i remains vacant, and $t_h$ denotes the time threshold. This reward structure for proactive relocation not only aims to minimize users' waiting time but also improves overall system efficiency. For example, quicker matches within the time threshold result in a more negative $t_i - t_h$, allowing agents to earn a higher positive reward of up to a maximum of 20. However, if matches occur beyond the time threshold, $t_i - t_h$ becomes positive, leading to a greater negative penalty, down to a minimum of -20.

In multi-agent settings, independently learning policy gradient methods such as Q-learning and DQN perform poorly, as each agent's policy changes to overwhelm the others during training, resulting in a non-stationary environment. To address this issue and achieve convergence of the algorithm, the centralized training and decentralized execution framework is adopted. An actor-critic method is applied using a multi-agent deep deterministic policy gradient algorithm. The actor and critic networks are set to be the same for all agents [34].

### III. APPLICATION

The proposed model was evaluated using field data from the Athens network obtained from GTFS, an open dataset provided by Athens Public Transit. The network encompasses an area of approximately 6 km by 6 km, as shown in Fig. 3. Public transportation comprises trams, metros, and buses, with frequencies of 20 minutes, 6 minutes, and 10 minutes, respectively. A total of 400 RH vehicles are operated from 7 depots.

During a 2-hour observation period, 22,980 users are generated, resulting in an average departure rate of 3.19 users per second. The simulation starts with a 30-minute warming-up period to stabilize traffic operations. Subsequently, a disruption is introduced, lasting for one hour. During the disruption period, stations of a metro line are closed. To facilitate agent-based traffic dynamics, Multi-modal Network Modelling and Simulations (MnMS) is applied in this study [40].

<figure><img src="image_4.png" /><figcaption>Fig. 3. Athens network illustrating the integration of car, bus, metro, and tram links, along with ride-hailing depots across a 6 km x 6 km area.</figcaption></figure>

### IV. NUMERICAL RESULTS

Disruption scenarios with accurate demand predictions are implemented as a preliminary analysis to assess the resilience of transportation systems, as shown in Fig. 4. The performance patterns of the systems demonstrate differences among centralized, decentralized, and MARL-based approaches. Performance declines occur during disruptions, and recovery to the original state is achieved following these disruptions. In particular, the centralized strategy showed the steepest performance decline. Both the centralized and decentralized approaches reached their lowest performance levels at different times, although at the same performance level. The MARL approach showed an intermediate performance decline, resulting in the smallest overall reduction. Therefore, it can be concluded that the MARL approach is the most resilient system against disruptions.

<figure><img src="image_5.png" /><figcaption>Fig. 4. System performance under accurate demand prediction during disruptions, comparing resilience across rebalancing strategies.</figcaption></figure>

### V. CONCLUSION

This study assesses the resilience of RH rebalancing strategies in multi-modal transportation systems. The centralized and decentralized approaches exhibit trade-offs in system performance. The proposed MARL approach demonstrates the best performance while also enhancing overall resilience.

Future work should focus on reducing uncertainties in demand prediction, particularly noise and delays, to further enhance the robustness of RH rebalancing systems. Additionally, transferability of RH rebalancing models could be
explored to create more precise and robust systems. We will compare results between the Athens network and the Manhattan network to investigate critical factors influencing transferability and generalizability.

## ACKNOWLEDGMENT

This research has received funding from the European Union's Horizon Europe research and innovation program under Grant Agreement no. 101103808 (ACUMEN).

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