Spatial Modeling and Analysis of Vehicular Networks

Through vehicle-to-vehicle communication (V2V), vehicles can exchange information required for safety alerting other vehicles in their vicinity. Due to the mission-critical nature of safety applications, high reliability is a key requirement of V2V systems. Reliability is the probability that a V2V link can sustain a certain target data rate. It depends on the locations of transmitting and receiving vehicles and interferers, street geometry, and wireless medium. The reliability results obtained by conducting a large number of trials in the real world fail to provide crisp insights into the effects of network design parameters on reliability despite their high costs. We aim to complement/reduce these large-scale experiments by applying mathematical tools from stochastic geometry to (i) model vehicular networks, and (ii) analyze the reliability of V2V communication. In particular, we introduce the notion of model equivalence, which shows that the number of models can be drastically reduced to only a few classes. Also, we prove that many existing models can be substantially simplified to the proposed transdimensional models with virtually no loss in accuracy. Furthermore, we investigate the meta distribution (MD) of the signal-to-interference ratio (SIR), which is a much sharper performance metric than the SIR distribution that is usually studied. The SIR MD answers questions such as 'what fraction of the V2V links are 99% reliable if the target data rate is 10 Mbps?' This metric is the key towards designing V2V networks with guaranteed reliability.

With respect to the broadcast communication, we formulate the binned meta distribution of the SIR, which answers questions like 'what fraction of the V2V links that are in the distance range of 100-200 m are 99% reliable if the target data rate is 10 Mbps?' The binned variant of the MD provides insights into the effective range for reliable broadcast communication. Having the binned SIR MD as the performance metric, we compare different stochastic geometry models to system-level simulations. The Poisson point process-based vehicular networks rank the highest in terms of analytical tractability with loose approximations to system-level simulations; the Matérn hard-core process-based models provide tight approximations but are highly intractable; the determinantal point process-based models rank the highest in terms of accuracy with good tractability.