An epidemiological diffusion framework for vehicular messaging in general transportation networks

Emerging Vehicle-to-Vehicle (V2V) technologies are expected to significantly contribute to the safety and growth of shared transportation provided challenges towards their deployment can be overcome. This paper focuses on one such challenge: characterizing the fraction of vehicles which have received a message, as a function of space and time, and operating under different traffic and communication conditions. V2V technologies bridge two infrastructures: communication and transportation. These infrastructures are interconnected and interdependent. To capture this inter-dependence, which may vary in time and space, we propose a new methodology for modeling information propagation between V2V-enabled vehicles. The model is based on a continuous-time Markov chain which is shown to converge, under appropriate conditions, to a set of clustered epidemiological differential equations. The fraction of vehicles which have received a message, as a function of space and time may be obtained as a solution of these differential equations, which can be solved efficiently, independently of the number of vehicles. Such characterizations can form the basis of assessing several attributes of V2V systems, some of which we demonstrate. The characterizations lend themselves to a variety of generalizations and capture various interdependencies between communication and mobility. As tests of the model we provide applications both in real-world settings using microscopic traffic traces and in postulated scenarios of outages and system perturbations: we find good model agreement with microscopic trajectory from two actual trajectory datasets, as well as a synthetic trajectory dataset generated from the origin/destination matrix.