Routing autonomous vehicles in congested transportation networks: structural properties and coordination algorithms


This paper considers the problem of routing and rebalancing a shared fleet of autonomous (i.e., self-driving) vehicles providing on-demand mobility within a capacitated transportation network, where congestion might disrupt throughput. We model the problem within a network flow framework and show that under relatively mild assumptions the rebalancing vehicles, if properly coordinated, do not lead to an increase in congestion (in stark contrast to common belief). From an algorithmic standpoint, such theoretical insight suggests that the problems of routing customers and rebalancing vehicles can be decoupled, which leads to a computationally-efficient routing and rebalancing algorithm for the autonomous vehicles. Numerical experiments and case studies corroborate our theoretical insights and show that the proposed algorithm outperforms state-of-the-art point-to-point methods by avoiding excess congestion on the road. Collectively, this paper provides a rigorous approach to the problem of congestion-aware, system-wide coordination of autonomously driving vehicles, and to the characterization of the sustainability of such robotic systems.

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  1. 1.

    For any subset of nodes \(\mathcal {S}\subseteq \mathcal {V}\), we define a cut \((\mathcal {S}, \bar{\mathcal {S}})\subseteq \mathcal {E}\) as the set of edges whose origin lies in \(\mathcal {S}\) and whose destination lies in \(\bar{\mathcal {S}}=\{\mathcal {V}\setminus \mathcal {S}\}\). Formally, \((\mathcal {S},\bar{\mathcal {S}}):=\{(u,v)\in \mathcal {E}: u\in \mathcal {S}, v \in \bar{\mathcal {S}}\}\).

  2. 2.

    The source code for the modified taxi extension is available at


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The authors would like to thank Zachary Sunberg for his analysis on the road network symmetry of U.S. cities.

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Correspondence to Federico Rossi or Marco Pavone.

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This is one of several papers published in Autonomous Robots comprising the “Special Issue on Robotics Science and Systems”.

An earlier version of this paper was presented at the Robotics: Science and Systems Conference, 2016. This extended and revised version includes a full proof of all theorems and lemmas presented in the paper. It also includes a significantly extended simulation section, including a numerical investigation of the capacity-symmetry of major U.S. cities and a characterization of the performance of the proposed real-time algorithm with a state-of-the-art microscopic agent-based simulator, MATSim. This research was supported by the National Science Foundation under CAREER Award CMMI-1454737, the Toyota Research Institute (TRI), and the Dr. Cleve B. Moler Stanford Graduate Fellowship. This article solely reflects the opinions and conclusions of its authors and not NSF, TRI, or any other Toyota entity. Rick Zhang worked on this paper while he was a Ph.D. student at Stanford University.

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Rossi, F., Zhang, R., Hindy, Y. et al. Routing autonomous vehicles in congested transportation networks: structural properties and coordination algorithms. Auton Robot 42, 1427–1442 (2018).

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  • Self-driving cars
  • Intelligent transportation systems
  • Vehicle routing
  • Autonomous systems