Most existing models for information flow propagation in a vehicle-to-vehicle (V2V) communications environment are descriptive. They lack capabilities to control information flow, which may preclude their ability to meet application needs, including the need to propagate different information types simultaneously to different target locations within corresponding time delay bounds. This study proposes a queuing-based modeling approach to control the propagation of information flow of multiple classes. Two control parameters associated with a vehicle are leveraged to control the propagation performance of different information classes. A two-layer model is developed to characterize the information flow propagation wave (IFPW) under the designed queuing strategy. The upper layer is formulated as integro-differential equations to characterize the spatiotemporal information dissemination due to V2V communication. The lower layer characterizes the traffic flow dynamics using the Lighthill-Whitham-Richards model. The analytical solution of the asymptotic density of informed vehicles and the necessary condition for existence of the IFPW are derived for homogeneous traffic conditions. Numerical experiments provide insights on the impact of the mean communication service rate on information spread and its spatial coverage. Further, a numerical solution method is developed to solve the two-layer model, which aids in estimating the impacts of the control parameters in the queuing strategy on the IFPW speed under homogeneous and heterogeneous conditions. The proposed modeling approach enables controlling the propagation of information of different information classes to meet application needs, which can assist traffic managers to design effective and efficient traffic management and control strategies under V2V communications.