Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective (1404.4391v1)

Abstract: In this paper we present and analyze a queueing-theoretical model for autonomous mobility-on-demand (MOD) systems where robotic, self-driving vehicles transport customers within an urban environment and rebalance themselves to ensure acceptable quality of service throughout the entire network. We cast an autonomous MOD system within a closed Jackson network model with passenger loss. It is shown that an optimal rebalancing algorithm minimizing the number of (autonomously) rebalancing vehicles and keeping vehicles availabilities balanced throughout the network can be found by solving a linear program. The theoretical insights are used to design a robust, real-time rebalancing algorithm, which is applied to a case study of New York City. The case study shows that the current taxi demand in Manhattan can be met with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi fleet). Finally, we extend our queueing-theoretical setup to include congestion effects, and we study the impact of autonomously rebalancing vehicles on overall congestion. Collectively, this paper provides a rigorous approach to the problem of system-wide coordination of autonomously driving vehicles, and provides one of the first characterizations of the sustainability benefits of robotic transportation networks.

• The paper introduces a novel queueing-theoretical model that represents MOD systems as closed Jackson networks with passenger loss indicators.
• The paper employs a linear programming approach to derive an optimal rebalancing algorithm that minimizes vehicle redistribution while ensuring balanced service.
• The application to NYC taxi demand demonstrates that around 8,000 autonomous vehicles can achieve efficient fleet management, reducing reliance on traditional taxis.

Overview of "Control of Robotic Mobility-On-Demand Systems: A Queueing-Theoretical Perspective"

The paper by Rick Zhang and Marco Pavone introduces an analytical framework for studying autonomous Mobility-On-Demand (MOD) systems through a queueing-theoretical approach. This framework specifically evaluates MOD systems where autonomous vehicles (AVs) provide transport within urban areas, incorporating a self-rebalancing mechanism to maintain service quality across the network. The research casts the autonomous MOD system into a closed Jackson network model infused with passenger loss indicators to evaluate service dynamics and network balance.

Key Contributions

The paper's contributions can be summarized as follows:

1. Queueing-Theoretical Model: The research presents a model using the Jackson network framework, a well-established structure in queueing theory, to conceptualize and analyze MOD systems with AVs. The problem of rebalancing vehicles is framed in this context to ensure balanced vehicle availability across the network.
2. Optimal Rebalancing Algorithm: It demonstrates that a linear programming approach can yield an optimal rebalancing algorithm. This algorithm minimizes the number of rebalancing vehicles while maintaining network-wide availability balance, which is crucial for practical implementation in dynamic environments like urban settings.
3. Case Study Application: In applying the theoretical insights to New York City's taxi demand, the findings suggest that a fleet of approximately 8,000 autonomous vehicles could meet current demand levels, comprising about 60% of the current manual taxi fleet size. This number reflects concentrated network efficiency gains by employing AVs with an intelligent rebalancing system.
4. Model Extension to Congestion: The analysis is extended to address congestion effects. The addition of rebalancing vehicles impacts the overall congestion of the network, and the paper demonstrates that rebalancing can generally be managed strategically to minimize disruption, even in congested systems.

Theoretical and Practical Implications

The research carries significant implications in both theory and practice. From a theoretical point of view, it provides a stochastic framework that addresses core operational dynamics and service balance in an autonomous MOD system, an area that has seen limited paper. The paper connects stochastic fluctuations in customer arrivals and vehicle distribution to real-time service quality metrics, like vehicle availability and customer wait times. Practically, the insights on fleet size reduction and efficiency drive a compelling narrative for advanced urban transport solutions with AVs, embedding sustainability and effective space utilization within city planning paradigms.

Future Developments

The paper opens several avenues for future development:

• Integration of Congestion-Aware Routing: Further exploration is needed to develop routing strategies that not only maintain balance across stations but also optimize road utilization by minimizing congestion impacts, leveraging current vehicle-state information actively during routing decisions.
• Incorporation of Multimodal Transport: Future research could examine the combined effects of MOD systems with other public transport systems to facilitate comprehensive urban mobility solutions.
• Algorithm Scalability and Real-World Testing: Investigating the applicability of the proposed algorithms to other urban environments, which differ in size and demand characteristics, will enrich the potential generalizability of the findings.
• Adaptive Rebalancing Policies: Extending the model to incorporate adaptive, real-time data-driven policies that can react to unpredictable demand fluctuations or road conditions.

This paper is an important contribution to the field of AI and robotic systems in transportation, constructing a robust theoretical framework that tangibly ties into real-world applications, thereby facilitating the shift towards efficient, intelligent urban mobility solutions using AVs.