Safe and Stabilizing Distributed Multi-Path Cellular Flows

TL;DR

This paper introduces a formal model for distributed traffic control in partitioned environments, ensuring safety and progress despite failures, with proofs and simulations demonstrating its effectiveness for multi-path, multi-target scenarios.

Contribution

It presents a novel distributed traffic control protocol that guarantees safety and self-stabilization in the presence of failures, with formal proofs and simulation validation.

Findings

Protocol guarantees minimum separation even during failures.

Self-stabilization occurs after failures cease for single-target scenarios.

Throughput depends on entity velocity, safety distance, and path complexity.

Abstract

We study the problem of distributed traffic control in the partitioned plane, where the movement of all entities (robots, vehicles, etc.) 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 coordinating robot swarms and the intelligent highway system. We present a formal model of a distributed traffic control protocol that guarantees minimum separation between entities, 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 entities 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 entities 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 distributed traffic control protocols. We present simulation results that provide estimates of throughput as a function of entity velocity, safety separation, single-target path complexity, failure-recovery rates, and multi-target path complexity.