# A Middleware-Based Approach for Multi-Scale Mobility Simulation
## 2 Literature Review
### Simulation Scales  
Mobility simulations are traditionally classified as microscopic, mesoscopic, or macroscopic, depending on the level of details of the represented entities and the chosen traffic model. However, these terms do not always refer to the same concepts which often depend on the context or use case. The author in [31] provides a definition of four simulation scales:  
* Macroscopic scale: this scale uses traffic flows and only aggregate variables such as vehicle density and average speed over an arc of the network. Lateral movements such as lane changes are not modeled.
* Mesoscopic scale: This scale also works with traffic flows but also uses probability functions to determine the possibility of a vehicle at a certain position, a certain time, and a certain speed.
* The microscopic scale: This scale represents individual vehicles with their own trajectory and speed. The behavior of the vehicles is modeled by a car-following model or by a cellular transmission model.
* Picoscopic scale: This scale represents individual vehicles with their own trajectory and speed. In contrast to the microscopic scale, the speed and trajectory of a vehicle are in two dimensions, on the road axis and laterally. In the most detailed models, the vehicle and the driver are two separate entities interacting with each other.  
The authors in [32] propose avoiding the use of such rigid scales and to classify the simulations based on their characteristics. The authors consider two characteristics: the representation of the entities (which can be individual or as a flow) and the traffic model (which can be individual or global). This classification is arguable since the representation of travelers and the traffic model are often linked. For instance, simulations that model travelers as flows necessarily have a global traffic model. However, the idea to classify simulations using their characteristics is interesting. Based on this idea, we determine three characteristics to determine the scale of a simulation:  
1. The representation of the travelers (noted \(\omega\)). Three main modalities are defined for this scale: individual representation (called microscopic by abuse of language), representation by groups of individuals (called mesoscopic), and representation by flow (called macroscopic).
2. Space (noted \(\sigma\)). Several modalities are possible for this dimension. We could refer to the levels of detail of the OGC CityGML standard [33], for which the authors in [34]specify for transportation modeling. However, mobility simulations rarely explicitly refer to the CityGML standard, so we decide to refer instead to two main modalities used in simulation and traffic assignment, following the existing layers in commercial maps: either a very detailed representation of networks (including small streets and directional restrictions, i.e., one-way restrictions, turning bans, etc.), or an aggregated representation, which represent only the main traffic axes.
3. Time (noted \(\theta\)). We identify three main modalities corresponding to the orders of magnitude of the represented time dimension. The order of seconds corresponds to very detailed mobility simulations, the order of minutes corresponds to dynamic traffic assignment models, and the order of hours corresponds to static assignment models (considering stationary time, usually referring to peak hours).  
Unlike [32], we choose to not consider the traffic model as a characteristic because it depends on the three other axes. Indeed, the flow representation does not allow a car-following model, a time step of one hour is too long to consider local interaction between pedestrians and a two-dimensional movement cannot be considered if we are using an aggregated graph with a one-dimensional axis.