X Safe and Stabilizing Distributed Traffic Control TAYLOR T. JOHNSON, University of Illinois at Urbana-Champaign SAYAN MITRA, University of Illinois at Urbana-Champaign We study the problem of distributed traffic control in the partitioned plane, where the movement of all entities (vehicles) within each partition (cell) is coupled. Establishing liveness in such systems is challenging, but such analysis will be necessary to apply such distributed traffic control algorithms in applications like the intelligent highway system and for coordinating robot swarms. We present a distributed traffic control protocol that guar- antees minimum separation between vehicles, even as some cells fail. Once new failures cease occurring, in the case of a single target, the protocol is guaranteed to self-stabilize and the vehicles with feasible paths to the target cell make progress towards it. For multiple targets, failures may cause deadlocks in the system, so we identify a class of non-deadlocking failures where all vehicles are able to make progress to their respective targets. The algorithm relies on two general principles: temporary blocking for maintenance of safety and local geographical routing for guaranteeing progress. Our assertional proofs may serve as a template for the analysis of other dis- tributed traffic control protocols. We present simulation results that provide estimates of throughput as a function of vehicle velocity, safety separation, single-target path complexity, failure-recovery rates, and multi-target path complexity. Categories and Subject Descriptors: C.2.4 [Distributed Systems]: Distributed Applications General Terms: Design, Algorithms, Performance ACM Reference Format: Johnson, T. T.and Mitra, S.. 201x. Safe and Stabilizing Distributed Traffic Control. ACM Trans. Autonom. Adapt. Syst. X, X, Article X ( 201X), 30 pages. DOI = 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000 1. INTRODUCTION Highway and air traffic flows are nonlinear switched dynamical systems that give rise to complex phenomena such as abrupt phase transitions from fast to sluggish flow [Helbing and Treiber 1998; Kerner 1998; Daganzo et al. 1999]. Our ability to monitor, predict, and avoid such phenomena can have a significant impact on the reliability and capacity of physical traffic networks. Traditional traffic protocols, such as those implemented for air traffic control are centralized [Nolan 1994]—a coordinator periodically collects information from the vehicles, decides and disseminates waypoints, and subsequently the vehicles try to blindly follow a path to the waypoint. Wireless vehicular networks [Borgonovo et al. 2003; Karpiriski et al. 2006; Manvi et al. 2009; Azimi et al. 2011] and autonomous vehi- cles [Thrun et al. 2007; Urmson et al. 2008] present new opportunities for distributed traffic monitoring [Yang et al. 2004; Misener et al. 2005; Hoh et al. 2008] and control [Girard et al. 2001; Mamei et al. 2003; Abbott et al. 2004; Kelly and Di Marzo Serugendo 2007; Kowshik et al. 2008; Dresner and Stone 2008]. While these protocols may still rely on some central- ized coordination, they should scale and be less vulnerable to failures compared to their This work is supported by the National Science Foundation under CAREER Grant No. 1054247. Author’s ad- dresses: T. T. Johnsonand S. Mitra, Coordinated Science Laboratory, Department of Electrical and Computer En- gineering, University of Illinois at Urbana-Champaign. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted with- out fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy other- wise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. © 201X ACM 1556-4665/201X/-ARTX $10.00 DOI 10.1145/0000000.0000000 http://doi.acm.org/10.1145/0000000.0000000 ACM Transactions on Autonomous and Adaptive Systems, Vol. X, No. X, Article X, Publication date: 201X.