This work presents the modeling methodology of the iTETRIS platform to integrate and simulate ITS applications. iTETRIS is a modular and open-source simulation platform composed of four key modules: the network simulator ns-3, the traffic simulator SUMO, an ITS (Intelligent Transportation System) application simulator, and a central federating module called iCS. Our contribution is twofold: First, we propose a methodology to model and simulate ITS applications with iTETRIS around three main mechanisms: (i) message management with generic open APIs based on subscription/result container mechanisms (ii) data management with the integration of an application facilities layer in the iCS, including a local dynamic map (LDM), (iii) application management with an ITS application simulator including one or more application logics. Second, we apply this methodology to implement the following four ITS applications: dynamic route planning, bus lane management, emergency vehicle, and contextual speed adaptation. We describe their integrations in iTETRIS, including a characterization of their interactions with the iCS, and illustrate the benefits of these ITS applications on traffic efficiency, gasoline consumption, or air pollutant emissions.