The Transdimensional Poisson Process for Vehicular Network Analysis

TL;DR

This paper introduces the transdimensional Poisson process (TPPP) as a simplified yet accurate model for analyzing vehicular networks, enabling tractable computation of the SIR meta distribution and network congestion control.

Contribution

The paper proposes the TPPP model that combines 1D and 2D PPPs for vehicular network analysis, improving accuracy over existing models and facilitating congestion management.

Findings

TPPP provides good approximations to complex street-based models.

Accuracy of TPPP improves with shadowing effects.

MD analysis enables effective network congestion control.

Abstract

A comprehensive vehicular network analysis requires modeling the street system and vehicle locations. Even when Poisson point processes (PPPs) are used to model the vehicle locations on each street, the analysis is barely tractable. That holds for even a simple average-based performance metric -- the success probability, which is a special case of the fine-grained metric, the meta distribution (MD) of the signal-to-interference ratio (SIR). To address this issue, we propose the transdimensional approach as an alternative. Here, the union of 1D PPPs on the streets is simplified to the transdimensional PPP (TPPP), a superposition of 1D and 2D PPPs. The TPPP includes the 1D PPPs on the streets passing through the receiving vehicle and models the remaining vehicles as a 2D PPP ignoring their street geometry. Through the SIR MD analysis, we show that the TPPP provides good approximations to the more cumbrous models with streets characterized by Poisson line/stick processes; and we prove that the accuracy of the TPPP further improves under shadowing. Lastly, we use the MD results to control network congestion by adjusting the transmit rate while maintaining a target fraction of reliable links. A key insight is that the success probability is an inadequate measure of congestion as it does not capture the reliabilities of the individual links.