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Spatiotemporal Analysis of Shared Situation Awareness among Connected Vehicles

Seungmo Kim

TL;DR

The paper addresses the latency of forming Shared Situation Awareness (SSA) in distributed V2X networks by developing a stochastic framework based on a 2D Poisson point process for vehicle locations and a hop-based propagation model. It derives a closed-form Gamma distribution for the SSA completion time, $H_{ssa} \sim \text{Gamma}(Nk, c\lambda)$, and demonstrates NP-complete characteristics for the cooperative SSA construction problem via a subset-sum analogy. Numerical simulations corroborate the theoretical results and reveal that higher vehicle density reduces SSA latency, aiding compliance with strict ITS safety-message deadlines. The work provides design guidance for ITS deployments and enables latency-aware safety communications across varying traffic densities.

Abstract

Shared situation awareness (SSA) has been garnering explosive interest in various applications for intelligent transportation systems (ITS). In addition, the delay-constrained nature of supporting vehicular networks makes it critical to precisely analyze the performance of a SSA procedure. Extending the relevant literature, this paper provides an analysis framework that evaluates the performance of SSA in spatial and temporal aspects simultaneously. Specifically, this paper provides a closed-form probability distribution for the length of time taken for constitution of a SSA among a group of connected vehicles. This paper extends the calculation to investigation of feasibility of SSA in supporting various types of safety messages defined by the SAE J2735.

Spatiotemporal Analysis of Shared Situation Awareness among Connected Vehicles

TL;DR

The paper addresses the latency of forming Shared Situation Awareness (SSA) in distributed V2X networks by developing a stochastic framework based on a 2D Poisson point process for vehicle locations and a hop-based propagation model. It derives a closed-form Gamma distribution for the SSA completion time, , and demonstrates NP-complete characteristics for the cooperative SSA construction problem via a subset-sum analogy. Numerical simulations corroborate the theoretical results and reveal that higher vehicle density reduces SSA latency, aiding compliance with strict ITS safety-message deadlines. The work provides design guidance for ITS deployments and enables latency-aware safety communications across varying traffic densities.

Abstract

Shared situation awareness (SSA) has been garnering explosive interest in various applications for intelligent transportation systems (ITS). In addition, the delay-constrained nature of supporting vehicular networks makes it critical to precisely analyze the performance of a SSA procedure. Extending the relevant literature, this paper provides an analysis framework that evaluates the performance of SSA in spatial and temporal aspects simultaneously. Specifically, this paper provides a closed-form probability distribution for the length of time taken for constitution of a SSA among a group of connected vehicles. This paper extends the calculation to investigation of feasibility of SSA in supporting various types of safety messages defined by the SAE J2735.
Paper Structure (13 sections, 3 theorems, 8 equations, 6 figures)

This paper contains 13 sections, 3 theorems, 8 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model
  4. Geometry
  5. Networking among Vehicles
  6. Analyses on SSA Completion Time
  7. Cooperative SSA
  8. Latency for SSA
  9. Numerical Results
  10. Parameters and Setup
  11. Confirmation of Theorem \ref{['theorem_gamma_sum']}
  12. Variation of Vehicle Density $\lambda$
  13. Concluding Remarks

Key Result

Lemma 1

(Distribution of the number of vehicles within a subset of $\mathbb{A}^2$) Let the transmission range of an arbitrary vehicle $i$ be denoted by $\mathbb{A}_{i}^2, \space \forall i \in \mathbb{N}$, which, as such, yields $\mathbb{A}_{i}^2 \in \mathbb{A}^2$. Given that the number of vehicles counted i

Figures (6)

  • Figure 1: A single snapshot of the mobile V2X system for scenario one with $\lambda$ = 100/$\left|\mathbb{A}^2\right|$ and $\left(W,D\right)$ = (1000 m, 1000 m) (The black square at the origin is the tagged vehicle, and the black circle around it indicates the transmission range of the tagged vehicle. A blue circle indicates a vehicle neighboring to the tagged vehicle, while a green circle gives a vehicle that is outside of the tagged vehicle's transmission range. The red star inside the circle is the target of awareness by the tagged vehicle.)
  • Figure 2: Union and intersection of shared knowledge among multiple nodes (An example with the detection radius of 75 m by each vehicle.)
  • Figure 3: Comparison of sampling and PDF of the Poisson($\rho\lambda$) for proof of Lemma \ref{['lemma_poisson_subset']}
  • Figure 4: Abstraction of constitution of a path until achievement of a SSA
  • Figure 5: Confirmation of Theorem \ref{['theorem_gamma_sum']} with simulation results: PDF of the length of time taken to reach a full SSA (The PDF shows an example of $\text{Gamma}\left(4,1/50\right)$.)
  • ...and 1 more figures

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Theorem 1