Modeling the Impact of Traffic Signals on V2V Information Flow

Information propagation in V2V-enabled transportation networks is highly influenced by both vehicle mobility and wireless communication. The mobility patterns and communication conditions are not only heterogeneous, but also vary both temporally and spatially. In particular, realistic traffic flow changes with time, exhibiting sharp time-triggered transitions, due to external factors such as traffic lights, unpredictable disruptions (e.g., accidents), and planned disruptions (e.g., road-block). More specifically, traffic signals cause traffic synchronization, due to vehicles stopping during the red phase, and starting almost simultaneously during the green phase, which fundamentally alters the dynamics of V2V message propagation in a complex manner. In this paper, we propose a mathematical framework, starting from a continuous-time Markov chain, that characterizes the fraction of vehicles that have received a message over time and space in an arbitrary road network even when the traffic flow exhibits sharp time-triggered transitions. Our framework can accommodate arbitrary traffic synchronization patterns corresponding for example to the presence of an arbitrary number of traffic signals. The stochastic model for V2V message flow converges to a set of differential equations as the number of vehicles increases. The analytical characterization lends itself to a fast computation regardless of the number of vehicles and traffic synchronization patterns, while vehicular network simulators can only realistically simulate small-scale transportation networks. We find that V2V simulations of a statistical model with traffic synchronization and simulation of communications applied on a synthetic traffic trace well match our model solution.