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A Knowledge-Based Analysis of Intersection Protocols

Kaya Alpturer, Joseph Y. Halpern, Ron van der Meyden

TL;DR

The paper tackles fault-tolerant, knowledge-based protocol design for vehicle intersections, formalizing the problem with safety and liveness guarantees while optimizing throughput under various fault models. It develops a comprehensive framework combining epistemic reasoning (via runs-and-systems and $K_i$), information-exchange protocols, and adversarial dynamics, and introduces lexicographic optimality as a strong performance criterion. By constructing knowledge-based programs that implement intersection policies, the authors demonstrate existences and uniqueness of lexicographically optimal implementations in synchronous contexts, including scenarios with no communication and with limited communication. The approach generalizes distributed mutual exclusion to unbounded, topologically diverse intersections and provides architecture-independent guidance for robust, scalable intersection management in V2V systems.

Abstract

The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run protocols among themselves to determine right of way. In this paper, we define the intersection problem to model this scenario abstractly, without any assumptions on the specific structure of the intersection or a bound on the number of vehicles. Protocols solving the intersection problem must guarantee safety (no collisions) and liveness (every vehicle eventually goes through). In addition, we would like these protocols to satisfy various optimality criteria, some of which turn out to be achievable only in a subset of the contexts. In particular, we show a partial equivalence between eliminating unnecessary waiting, a criterion of interest in the distributed mutual-exclusion literature, and a notion of optimality that we define called lexicographical optimality. We then introduce a framework to design protocols for the intersection problem by converting an intersection policy, which is based on a global view of the intersection, to a protocol that can be run by the vehicles through the use of knowledge-based programs. Our protocols are shown to guarantee safety and liveness while also being optimal under sufficient conditions on the context. Finally, we investigate protocols in the presence of faulty vehicles that experience communication failures and older vehicles with limited communication capabilities. We show that intersection protocols can be made safe, live and optimal even in the presence of faulty behavior.

A Knowledge-Based Analysis of Intersection Protocols

TL;DR

The paper tackles fault-tolerant, knowledge-based protocol design for vehicle intersections, formalizing the problem with safety and liveness guarantees while optimizing throughput under various fault models. It develops a comprehensive framework combining epistemic reasoning (via runs-and-systems and ), information-exchange protocols, and adversarial dynamics, and introduces lexicographic optimality as a strong performance criterion. By constructing knowledge-based programs that implement intersection policies, the authors demonstrate existences and uniqueness of lexicographically optimal implementations in synchronous contexts, including scenarios with no communication and with limited communication. The approach generalizes distributed mutual exclusion to unbounded, topologically diverse intersections and provides architecture-independent guidance for robust, scalable intersection management in V2V systems.

Abstract

The increasing wireless communication capabilities of vehicles creates opportunities for more efficient intersection management strategies. One promising approach is the replacement of traffic lights with a system wherein vehicles run protocols among themselves to determine right of way. In this paper, we define the intersection problem to model this scenario abstractly, without any assumptions on the specific structure of the intersection or a bound on the number of vehicles. Protocols solving the intersection problem must guarantee safety (no collisions) and liveness (every vehicle eventually goes through). In addition, we would like these protocols to satisfy various optimality criteria, some of which turn out to be achievable only in a subset of the contexts. In particular, we show a partial equivalence between eliminating unnecessary waiting, a criterion of interest in the distributed mutual-exclusion literature, and a notion of optimality that we define called lexicographical optimality. We then introduce a framework to design protocols for the intersection problem by converting an intersection policy, which is based on a global view of the intersection, to a protocol that can be run by the vehicles through the use of knowledge-based programs. Our protocols are shown to guarantee safety and liveness while also being optimal under sufficient conditions on the context. Finally, we investigate protocols in the presence of faulty vehicles that experience communication failures and older vehicles with limited communication capabilities. We show that intersection protocols can be made safe, live and optimal even in the presence of faulty behavior.
Paper Structure (11 sections, 2 theorems, 1 equation, 1 figure, 4 algorithms)

This paper contains 11 sections, 2 theorems, 1 equation, 1 figure, 4 algorithms.

Table of Contents

  1. Introduction
  2. Reasoning about knowledge
  3. Information-exchange protocols
  4. Adversary model
  5. Intersection Contexts
  6. Unnecessary waiting and optimality
  7. Intersection policies
  8. A Knowledge-Based Program with Lexicographically Optimal Implementations
  9. Implementing $\mathbf{P}$ when there is no communication
  10. Implementing $\mathbf{P}$ in a context with limited communication
  11. Discussion

Key Result

Lemma 11

For $\mathcal{F} \in \{CR, SO\}$, suppose that $(r,m)$ is a point of $P^\mathit{intent}$ in context $\gamma_\mathit{intent}(\mathcal{F})$, and let $i$ and $j$ be agents with $\mathit{front}_i(r,m) = \mathit{front}_j(r,m) = 1$ and $\mathit{lane}_j(r,m) \in [\mathit{next}(r,m),\mathit{lane}_i(r,m))$.

Figures (1)

  • Figure 1: An intersection with $\mathcal{L} = \{1,\dots,8\}$ where $\mathcal{L}_\mathit{in} = \{1,\dots,4\}$ and $\mathcal{L}_\mathit{out} = \{5,\dots,8\}$. There are currently 4 agents that have arrived in incoming lanes 2 and 3.

Theorems & Definitions (12)

  • Definition 1: unnecessary waiting
  • Definition 2: corresponding runs
  • Definition 3: domination
  • Definition 4: optimality
  • Definition 5: lexicographical domination
  • Definition 6: lexicographic optimality
  • Definition 7: intersection policy
  • Example 8
  • Example 9
  • Definition 10: efficient intersection policies
  • ...and 2 more