## 4 Results: Model Application and Experiments
### Parameters and Assumptions  
In this study, the runway sections with flexible pavement are considered. Each sample unit is assumed to have a width of 7.5 m and a length of 50 m, for a total area 375 m\({}^{2}\).  
This research works focuses on the \(Q=3\) performance indicator, namely the Residual Life (RL), the International Roughness Index (IRI) and the Pavement Condition Index (PCI).  
In accordance with the literature [43; 45; 46], the performance indicator values related to the best condition and the critical thresholds are, respectively, assumed to be equal to 20 and 0 years for RL, 0.7 and 3.60 m/km for IRI, and 95 e 25 for PCI. Note that the higher both the RL and PCI, the better the residual life and surface condition of the pavement under study. To make IRI consistent with the trend of the previous performance indicators, the reciprocal IRI indicator, hereinafter referred to as IRRI, is adopted for the subsequent analysis.  
Actually, all these indicators are connected to specific decay functions [47] and, since predictive degradation models are not easily transferable from one airport to another and considering that this study does not want to be specific for a single airport, theoretical time-dependent decay models are used. Specifically, the deterioration models of \(RL\) and \(IRRI\) are linear, while a non-linear relationship is assumed for PCI [42], as follows [15]:  
\[RL(t)=RL(t-1)-1\big{|}0\leq RL(t)\leq RL_{opt}=20\ years\ \forall t \tag{7}\]  
\[IRI(t)=IRI(0)+0.4\times t \tag{8}\]  
\[IRRI(t)=1/IRI(t) \tag{9}\]  
\[PCI(t_{0}+t)=-0.14(t_{0}+t)^{3}+2.28(t_{0}+t)^{2}-15(t_{0}+t)+100\big{|}PCI(t )\geq 0\ \forall t \tag{10}\]  
where \(t_{0}\) is a time reference value necessary to assess the PCI indicator at time zero. The relations described in (9) and (10) evaluate the functional conditions of the pavement in terms of longitudinal roughness and general distress conditions. For this study, their correlation is not in depth but, certainly, they are determined by the detected distresses. Referring to the M&R activities, in this research five types of M&R activities (\(I=\{0,\,1,\,2,\,3,\,4\}\)) have been taken into account [15]. It is assumed that it is possible to do only one intervention for each work-zone per year. Note that the so-called do-nothing activity (\(I=0\)) means that no M&R action is conducted in the critical work-zone at year \(t\) (\(x_{wt}=0\)). Below are the M&R activities hypothesized for this study (Figure 2).  
For all types of intervention, their definition and related effects are based on some laboratory studies on the materials used for the pavement in question. Regarding the residual life reported in the manuscript, it is the parameter related to the moduli of the existing and requalified pavement courses.  
Table 2 indicates the costs and effects of M&R activities. According to the Federal Aviation Administration [46], they depend on the materials used during the activities and the composition of the hypothesized pavement package.  
In the end, in accordance with the common airport practice, this study sets a short-term time horizon. More specifically, T is assumed to be equal to six years. Instead, the constraint of maintaining the performance indicators above the critical thresholds for a control time equal to (T + 2) years is considered in all the strategies described in Section 3.2. The only exception is in Strategy 5, due to the impossibility of eliminating the violations given the limited effects of possible actionable activities.