We introduce a general framework for the modeling and analysis of vehicular networks by defining street systems as random 1D subsets of $\mathbb {R}^{2}$ . The street system, in turn, specifies the random intensity measure of a Cox process of vehicles, i.e., vehicles form independent 1D Poisson point processes on each street. Models in this Coxian framework can characterize streets of different lengths and orientations forming intersections or T-junctions. The lengths of the streets can be infinite or finite and mutually independent or dependent. We analyze the reliability of communication for different models, where reliability is the probability that a vehicle at an intersection, a T-junction, or a general location can receive a message successfully from a transmitter at a certain distance. Further, we introduce a notion of equivalence between vehicular models, which means that a representative model can be used as a proxy for other models in terms of reliability. Specifically, we prove that the Poisson stick process-based vehicular network is equivalent to the Poisson line process-based and Poisson lilypond model-based vehicular networks, and their rotational variants.

中文翻译：

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车载网络的 Cox 模型：SIR 性能和等效性

我们通过将街道系统定义为 $\mathbb {R}^{2}$ 的随机一维子集，为车辆网络的建模和分析引入了一个通用框架。反过来，街道系统指定了车辆 Cox 过程的随机强度度量，即车辆在每条街道上形成独立的一维泊松点过程。该 Coxian 框架中的模型可以表征不同长度和方向的街道，形成交叉路口或丁字路口。街道的长度可以是无限的或有限的，并且相互独立或依赖。我们分析了不同模型的通信可靠性，其中可靠性是车辆在十字路口、丁字路口或一般位置可以成功从一定距离的发射器接收消息的概率。更多，我们引入了车辆模型之间的等效性概念，这意味着代表性模型可以用作其他模型在可靠性方面的代理。具体来说，我们证明了基于泊松棒过程的车辆网络等价于基于泊松线过程和基于泊松百合模型的车辆网络及其旋转变体。