Analysis of a Spatially Correlated Vehicular Network Assisted by Cox-distributed Vehicle Relays

TL;DR

The paper addresses reliability and throughput challenges in V2X networks where RSUs alone may be congested, by introducing a two-tier vehicular network with RSU-operated relays. It develops a tractable stochastic-geometry model where roads are modeled as a $Poisson$ line process and RSUs, relays, and users are $Cox$ point processes conditioned on the road network, capturing spatial correlation. The authors derive the association probabilities and SIR-based coverage probabilities for typical users and relays, and formulate the user throughput as a function of densities, bandwidths, and geometry, enabling design insights. The results offer practical guidance on relay density and spectrum allocation to achieve ultra-reliable or maximum throughput operation, and establish a foundation for extending the framework to more complex road topologies or clustering in future work.

Abstract

In vehicle-to-all (V2X) communications, roadside units (RSUs) play an essential role in connecting various network devices. In some cases, users may not be well-served by RSUs due to congestion, attenuation, or interference. In these cases, vehicular relays associated with RSUs can be used to serve those users. This paper uses stochastic geometry to model and analyze a spatially correlated heterogeneous vehicular network where both RSUs and vehicular relays serve network users such as pedestrians or other vehicles. We present an analytical model where the spatial correlation between roads, RSUs, relays, and users is systematically modeled via Cox point processes. Assuming users are associated with either RSUs or relays, we derive the association probability and the coverage probability of the typical user. Then, we derive the user throughput by considering interactions of links unique to the proposed network. This paper gives practical insights into designing spatially correlated vehicular networks assisted by vehicle relays. For instance, we express the network performance such as the user association, SIR coverage probability, and the network throughput as the functions of network key geometric variables. In practice, this helps one to optimize the network so as to achieve ultra reliability or maximum user throughput of a spatially correlated vehicular networks by varying key aspects such as the relay density or the bandwidth for relays.

Figures (11)

• Figure 1: Illustration of the proposed vehicular network with RSUs, relays, and users. Users may get messages directly from RSUs (right) or via relays (left).
• Figure 2: Illustration of the proposed network where $\lambda_l=2/\text{km}$, $\mu_s=2/\text{km}$, $\mu_r= 4/\text{km}$, and $\mu_u=10/\text{km}$.
• Figure 3: Illustration of the proposed network where $\lambda_l=5/\text{km}$, $\mu_s=2/\text{km}$, $\mu_r= 2/\text{km}$, and $\mu_u=5/\text{km}$.
• Figure 4: Illustration of the proposed network where $\lambda_l=10/\text{km}$, $\mu_s=2/\text{km}$, $\mu_r= 4/\text{km}$, and $\mu_u=10/\text{km}$.
• Figure 5: Illustration of the association probability of the typical user. The derived formula of Lemma \ref{['Theorem:2']} matches the simulation results. We use $\lambda_l=2$/km and $\mu_s=1$/km.

Theorems & Definitions (14)

• Remark 1
• Remark 2
• Example 1
• Remark 3
• Lemma 1
• Theorem 1
• Theorem 2
• Remark 4
• Corollary 1
• Theorem 3