*2.4. Prescription*

Once the modeling phase itself has been completed, the resulting model faces its application to a real ITS environment. It is at this stage when actions deriving from the data insights are defined/learned/decided, and when the actionability of the model can be best assessed. Yet, this stage is frequently overlooked in most ITS research, where most works conclude at presenting the good performance of a model; it is uncommon to find evaluations of a given model in terms of its final application in a certain environment. Are the actions that can be taken as a result of the outcome of a data-based model aimed at a strategic, tactical or operational decision making? Is the output of the data-based model able to support decisions made by transportation networks managers? Can the output be consumed directly without any need for further modeling, or exploited by means of a secondary modeling process aimed at optimizing the decision making process? This latter case can be exemplified, for instance, by the formulation of the decision making process as an optimization problem, in which actions are represented by the variables compounding a solution to the problem, and the output of the previous data-based modeling phase can be used to quantitatively estimate the quality or fitness of the solution. One of the most prominent examples of this prescription mode deals with routing problems, since they often use simulation tools or predictive models to assess the travel time, pollutant emissions or any other optimization objective characterizing the fitness of the tested routes [46,47]. Other examples of prescription based on data emerge in tactical and strategic planning, such as the modification of public transportation lines [48], the establishment of special lanes (e.g., taxi, bike) [49], the improvement of road features [50], the adaptive control of traffic signaling [51], the identification of optimal delivery (or pickup) routes for different kinds of transportation services [52], the incident detection and managemen<sup>t</sup> [53], learning for automated driving [54], or the design of sustainable urban mobility plans based on the current and future demand or the drivers' behavior [55,56].

In any of the above presented ITS cases, a data-based model should be equipped with a certain set of features that guarantee its actionability. For instance, if a traffic manager is not able to interpret a model or understand its outcome in terms of confidence, it can be hardly applied for practical decision making. When the model is used for adaptive control purposes (as in automated traffic light scheduling), the adaptability of the model to contextual changes is a key requirement for prescribed actions to be matched to the current traffic status [57]. Interestingly, some control techniques with a long history in the field (e.g., Stochastic Model Predictive Control, SMPC, [58]) serve as a good example of the triple-play between application requirements, decision making and data-based models. When dealing with the design of control methods in ITS, SMPC has been proven to perform efficiently in highly-complex systems subject to the probabilistic occurrence of uncertainties [59]. Specifically, SMPC leverages at its core data-based prediction modeling and low-complexity chance-constrained optimization to deal with control problems that impose that the method to be used must operate in real time. In this case, and in most actionable data-based workflows where decision making is formulated as an optimization problem, we note a clear entanglement between application requirements (e.g., real-time processing), decision making (low-complexity, dynamic optimization techniques) and data-based models (predictive modeling for system dynamics forecasting).
