1 Investigating the Resilience of Ride-hailing Fleet Management Strategies

2 for Seamless Multi-modal Transportation Systems

3

4 Euntak Lee

5 Univ. Eiffel, ENTPE, LICIT-ECO7, Lyon, France, F-69518

6 Email: euntak.lee@univ-eiffel.fr

7

8 Ludovic Leclercq

9 Univ. Eiffel, ENTPE, LICIT-ECO7, Lyon, France, F-69518

10 Email: ludovic.leclercq@univ-eiffel.fr

11

12 Word Count: 1,703 words

13

14 *Submitted [November 19, 2024]*

15

16

17

18 Acknowledgments:

19 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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22 **Statement of Significance (Relevance of Research):** As the worldwide ride-hailing (RH) industry grows, the integration of multi-modal transportation systems has become increasingly important to reduce traffic congestion and improve user mobility. Most RH studies used nominal scenarios with regular demand patterns. However, disruptions must be considered due to their negative impact on operational efficiency, such as longer travel times, higher costs, increased transfers, and more service delays. Therefore, this study investigates the resilience of RH fleet management strategies in multi-modal transportation systems against disruptions on train lines. Comparing the strategies provides critical insights for developing intermediate RH strategies to effectively manage disruptions and enhance the seamlessness of multi-modal transportation systems.

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33 Author contribution statement:

34 The authors confirm contribution to the paper as follows: study conception and design: Ludovic Leclercq, Euntak Lee; analysis and interpretation of results: Ludovic Leclercq, Euntak Lee; draft manuscript preparation: Ludovic Leclercq, Euntak Lee. All authors reviewed the results and approved the final version of the manuscript.

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# 1 INTRODUCTION

Most RH strategies were tested using a nominal scenario characterized by regular demand patterns. However, disruptions must be considered since they can deteriorate the operational efficiency of transportation systems (1). Disruptions can be categorized into two types: supply disruptions and demand disruptions. Supply disruptions lead to reductions in the availability of the road network, which may occur due to road accidents or the denial of mobility services. Demand disruptions relate to surges in transportation demand, such as during large sports events, strikes, or the arrival of mass public transportation. Excessive demand results in interruptions in system functioning due to limited supply capacity. For instance, public transportation routes might temporarily close, resulting in the discharge of numerous passengers at some stations. As a cascading effect, a surge in demand for limited alternative modes could lead all users to experience longer travel times, higher costs, increased transfers, and more service delays (2, 3). Therefore, it is crucial to assess the resilience of RH strategies against disruptions.

Indeed, the resilience of RH systems largely depends on fleet management strategies. Based on the number of predicted future ride requests, system operators direct RH vehicles to certain areas. Centralized or decentralized strategies for distributing the vehicles can affect operational efficiency. However, choosing a strategy is not a simple issue, especially with a large service area and considering the connectivity between multiple transportation modes (4). For the service area, on the one hand, a local supply-demand imbalance between drivers and passengers might occur irregularly. For connectivity, on the other hand, RH services play a crucial role as a supplementary mode in multi-modal transportation systems. Therefore, the resilience of RH strategies needs to be assessed in advance to enhance the systems. It is essential to investigate how RH services contribute to multi-modal transportation systems against disruptions.

Therefore, this study investigates the resilience of RH fleet management strategies in multi-modal transportation systems against disruptions on train lines. Two fleet management strategies, centralized and decentralized, are introduced to assess how the systems react when managed differently. Using a 900 km² toy urban network, a traffic simulation is conducted with a trip-based MFD model that includes multiple transportation modes such as trains, metros, buses, and RHs. The resilience of the RH systems is evaluated by considering average travel time and transfer waiting time. The results revealed that during the peak of disruption, the centralized strategy maintained a higher level of service but required a longer recovery time, whereas the decentralized strategy showed a lower service level but recovered more quickly. The centralized strategy showed higher system performance during a regular scenario, while the decentralized strategy showed better resilience during a disruption. A comparison between the two strategies provides critical insights for developing intermediate RH strategies to effectively manage disruptions and enhance the seamlessness of multi-modal transportation systems.

# 39 METHODOLOGY

To assess the resilience of RH services in the multi-modal transportation system, the modeling framework of this study is presented in three stages.

## 40 Multi-modal Transportation Systems

A basic structure for transportation systems is introduced. The fundamental component of the system is the road network. Once road segments are established, the movements of multiple transportation modes are defined using a trip-based MFD model. This model assigns the same
vehicle speed at the same time for all vehicles of similar modes driving in the same region (5, 6).

The speed values depend on the crowdedness of the region. Subsequently, the user origin-destination (OD) pairs are generated with temporal and spatial distributions. Based on these OD pairs, a pathfinding algorithm determines the potential shortest paths on the multi-modal transportation network for all considered modes. Trip lengths are derived from the list of path candidates.

## Ride-hailing (RH) Systems

### Centralized Strategy

For the centralized strategy, it operates a main operator that operates RH services for the whole network. Mathematical expressions for the centralized strategy are shown as follows.

Objective function

$$ \text{Maximize } Z = \sum_{r \in R} \sum_{v \in V} x_{rv} (U_o(r) + U_v(r)) \quad (1) $$

subject to,

$$ \sum_{v \in V} x_{rv} \le n_r, \quad \forall r \in R \quad (2) $$

$$ \sum_{r \in R} x_{rv} \le 1, \quad \forall v \in V \quad (3) $$

$$ x_{rv} \in \{0, 1\} \quad (4) $$

where,

$U_o(r)$: operator utility for service area $r$ ($r \in R$)

$U_v(r)$: utility of RH vehicle $v$ for service area $r$

$x_{rv}$: a binary variable whether area $r$ published a rebalance offer to vehicle $v$

$n_r$: a vacancy of service area $r$

### Decentralized Strategy

The decentralized strategy involves several local operators, each managing a separate service area. They negotiate with drivers to maximize their objectives. It is unlikely that any individual operator or driver will adhere to matching assignments based on social costs. They are primarily motivated by their self-interest and aim to maximize individual utilities (7). An auction-based Gale-Shapley matching method is adopted to optimize the rebalancing problem. This two-sided stable matching algorithm has been practically applied in a variety of real-world situations (8-10).

## Resilience Assessment

### System Performance

In this study, average travel time and waiting time are adopted for system performance. The mathematical equation for the system performance is described as follows:

$$ \text{System Performance } \mathcal{F}(t) = \bar{\mathcal{F}} - \sum_{\omega \in Q} \sum_{p \in P_w} \Gamma_p(t) \frac{n(P_w)}{n(Q)} \quad (5) $$

where, $\bar{\mathcal{F}}$ represents the baseline average travel time, and $\Gamma_p(t)$ denotes the waiting time after a passenger is matched with an RH vehicle for path $p \in P_w$ within the OD pair $\omega \in Q$. This metric considers the impact of system performance decrease and variations in OD demand (14).
1 Resilience

2 To represent the practical performance of the multi-modal transportation system against
3 disruptions, four indicators are defined in terms of resilience: vulnerability, adaptability,
4 robustness, and recoverability. The mathematical equations are shown in Equations 6–10.

5

6

$$
\text{Vulnerability} \quad R_1 = 1 - \frac{\int_{t_0}^{t_d} \mathcal{F}(t) dt}{\int_{t_0}^{t_d} \mathcal{F}_0(t) dt} \qquad (6)
$$

7

$$
\text{Adaptability} \quad R_2 = 1 - \frac{\int_{t_d}^{t_r} \mathcal{F}(t) dt}{\int_{t_d}^{t_r} \mathcal{F}_0(t) dt} \qquad (7)
$$

8

$$
\text{Robustness} \quad R_3 = 1 - \frac{\mathcal{H}(\xi)}{t_r - t_0} \qquad (8)
$$

9

$$
\text{Recoverability} \quad R_4 = \frac{t_r - t_d}{t_r - t_0} \qquad (9)
$$

10

$$
\text{Resilience} \quad R = \alpha_1 R_1 + \alpha_2 R_2 + \alpha_3 R_3 + \alpha_4 R_4 \quad (10)
$$

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12 Vulnerability in **Equation 6** represents the area gap resulting from a reduction in system
13 performance. This is calculated by integrating the system performance over the time interval from
14 the disruption start point $t_0$ to the low peak point $t_d$. Adaptability in **Equation 7** represents the
15 area gap that occurs during the recovery in performance. It is calculated over the time interval from
16 the low peak point $t_d$ and the fully recovered point $t_r$. Robustness in **Equation 8** represents the
17 ratio of the time duration when the system performed below a specified level. Recoverability in
18 **Equation 9** represents the ratio of the time duration that measures how quickly the system regained
19 its performance. Resilience in **Equation 10** is derived from a weighted sum of these four indicators.
20 In this study, all the weights are set to 1. In brief, more resilient systems have lower $R$ values.

20
# RESULTS

## Resilience of Multi-modal Transportation System

### Situation 1: Informed RH Operations (Real-time Disruption Updates)

**Figure 1** presents the comparison results between the two strategies with different fleet sizes. The indices tended to decrease as fleet size increased, indicating an improvement in resilience performance across all strategies. With all vehicles fully engaged in serving and pickups during disruptions, neither strategy had control over repositioning vehicles back to depots. These results reveal that a larger fleet size correlates with better performance. However, operating as many RH vehicles as possible is not ideal since traffic congestion and operating costs might increase due to an excess supply.

<figure><img src="image_1.png" /><figcaption>Figure 1 Resilience comparison with disruption updates across different fleet sizes</figcaption></figure>

### Situation 2: Uninformed RH Operations (No Disruption Alerts)

System operators manage RH services based on expected demands. Uncertainty in the number of future RH requests might exist, leading to inefficient operations. Therefore, the impacts of uncertainty in demand prediction were investigated. **Figure 2** illustrates the resilience indices when demand prediction for disruptions is not updated and thus the system is operated with regular demand patterns. The resilience results showed both similar and different patterns compared to the results when disruptions are reflected in demand patterns.
<figure><img src="image_2.png" /><figcaption>Figure 2 Resilience comparison between informed and uninformed disruption demand</figcaption></figure>
## Situation 3: Time Delay of Disruption Updates

There may be time delays in operators receiving information about disruptions. If a delay occurs, the cumulative number of users is reflected in the demand. For example, with a 20-minute delay, the operator applies regular demand predictions until informed. Once informed, the accumulated surge in users is added to the demand after 20 minutes. **Figure 3** represents the system's resilience with variations in fleet size and time delay for the disruption updates.

In **Figure 3(a)**, the resilience index for the centralized strategy increased overall compared to the real-time updated situation. This indicates that time delays negatively impact the centralized strategy more than the decentralized strategy. Moreover, the positive slopes of the contour lines show that increased time delays reduce the system resilience for a given fleet size. On the other hand, in **Figure 3(b)**, the contour lines for the decentralized strategy were more horizontal. It indicates that time delays have little impact on resilience. This is because local operators independently manage their respective small service areas with higher operational efficiency. These horizontal slopes also imply that fleet size predominantly affects system resilience more than time delays.

<figure><img src="image_3.png" /><figcaption>Figure 3 Resilience with time delays compared to the informed RH operations</figcaption></figure>

## CONCLUSION

This study investigates the resilience of RH fleet management strategies in multi-modal transportation systems against disruptions on train lines. Two fleet management strategies, centralized and decentralized, are introduced to assess how the systems react when managed differently. These strategies are implemented in a transportation system developed with a trip-based MFD model for user multi-modal trips.

The results provide insights into three main contributions. First, no significant differences are observed in the RH fleet management strategies during disruptions when the supply is insufficient. The operational limits are reached due to the lack of fleet size, with all vehicles fully engaged in either serving or picking up passengers. Second, when vehicles are sufficient, the two strategies show different patterns. During the peak of disruption, the centralized strategy maintains a higher level of service but requires a longer recovery time, whereas the decentralized strategy shows a lower service level but recovers more quickly. Additionally, the centralized strategy
outperforms during regular scenarios, while the decentralized strategy shows higher resilience against disruptions. Third, uncertainty or delays in demand prediction have significant impacts, while fleet size predominantly affects system resilience.

To develop more resilient RH fleet management strategies, improvements in both the centralized and decentralized strategies are required. In addition, intermediate strategies that integrate these two approaches can be developed. Furthermore, sensitivity to demand predictions should be further investigated.

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