# A Middleware-Based Approach for Multi-Scale Mobility Simulation
## 1 Introduction  
In their objective of optimizing the transport activity and minimizing its impact on the environment and the society, the transportation actors need support systems to assist them in their decisions. These decisions could concern the transportation supply (infrastructure [1], vehicles timetables [2], etc.), the transportation demand (traveler information [3], route guidance [4], pricing [5], etc.) or the regulation policies (speed limitations [6], access control [7], etc.). In this context, simulation is one of the important tools allowing the decision makers to test strategies and multiple scenarios without impacting the real traffic [8]. Some local mobility issues need a detailed representation of a neighborhood, such as crowd management [9]. However, simulating the only zone of interest is short-sighted and simulations should consider the surrounding areas, which can influence the status of the local area [10]. Indeed, an event occurring at a city or region scale might have a serious impact of the flows entering or leaving the considered neighborhood. Conversely, a high variation in the mobility status of the local area could have consequences on the regional scale. More generally, there exist many scenarios where one would need several simulations at different scales. For instance, we could think of a wide region simulation, in which we desire to zoom, and get more details, on certain areas; or a distributed mobility simulation platform that needs to synchronize the different computation units (as in [11]). The scale does not refer necessarily to the space dimension. It could concern the timedimension as well. For instance, we could have a running online simulation that needs a second faster-than-real-time simulation to test several scenarios before execution [12]. The scale could also refer to the represented entities (e.g., travelers) as well. Indeed, we could be interested in the individual representation of the travelers for a certain zone, and a flow representation for another zone, as in [13]. When dealing with different scales (space, time, or entities), the designer is tempted to create a new simulation allowing for representing properly the behavior of the modeled system, with all the necessary scales. However, provided the large number of possibilities for scales combinations, this would lead to an unnecessary explosion in the number of new simulation platforms. In the literature, authors have proposed several specific methods to couple simulations that consider different scales. To the best of our knowledge, there exists no proposal of a generic model to couple such simulations. Our purpose in this paper is to propose a model allowing for a reuse of existing simulation platforms to create multi-scale simulations. This model paves the way for interoperability between simulations and participates in time and resources efficiency in mobility models development.  
The remainder of this paper is structured as follows. We describe previous works on multi-scale simulations, on middleware, and we discuss simulations validity in Section 2. In Section 3, we define the middleware model, its components, operators, and functions. In Section 4, we provide algorithms for simulations scheduling in case of inter-dependency between them. We provide our experimental setup and results in Section 5. We discuss the applicability of our proposal in section and conclude the paper in Section 6.