# Characterizing Situations of Dock Overload in Bicycle Sharing Stations
## 3 Methodology
### Mining Occupancy Monitoring Patterns
#### 3.2.1 OMP Characterization  
OMPs allow to detect dock overload conditions in multiple stations. More specifically, OMPs represent the following situations:  
* Critical situation. The occupancy levels of a group of stations are frequently overloaded at the same time. In this case, simultaneously, all the stations in the group are fully occupied. * Intermittent situation. The occupancy levels of a group of stations are frequently overloaded in an alternate fashion. At a given point of time, some stations are fully occupied whereas the other \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Record IDentifier (RID)**} & \multicolumn{3}{c}{**Stations**} & \multicolumn{3}{c}{**Time**} \\ \cline{2-6}  & \(s_{1}\) & \(s_{2}\) & \(s_{3}\) & **Timestamp** & **Time Period** \\ \hline \(\text{RID}_{1}\) & Overloaded & Overloaded & Overloaded & \(t_{1}\) & \(TP_{1}\) \\ \(\text{RID}_{2}\) & Overloaded & Normal & Overloaded & \(t_{2}\) & \(TP_{1}\) \\ \(\text{RID}_{3}\) & Overloaded & Overloaded & Normal & \(t_{3}\) & \(TP_{1}\) \\ \(\text{RID}_{4}\) & Overloaded & Normal & Normal & \(t_{4}\) & \(TP_{1}\) \\ \(\text{RID}_{5}\) & Normal & Overloaded & Normal & \(t_{5}\) & \(TP_{2}\) \\ \(\text{RID}_{6}\) & Normal & Overloaded & Normal & \(t_{6}\) & \(TP_{2}\) \\ \(\text{RID}_{7}\) & Normal & Normal & Normal & \(t_{7}\) & \(TP_{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Example of Occupancy level datasetones are almost empty. At another point of time, the occupancy level of the same stations could be the opposite. To consider only sets of nearby stations, i.e., stations with a limited geographical distance in the city area, a spatial constraint can be enforced. Enforcing such a constraint implies that the OMPs consist of stations with maximal geographical distance below a given (analyst-provided) threshold. Critical situations are potentially harmful because, when all the stations in the group are overloaded, users cannot return the rented bicycles. In particular, the discovery of a group of overloaded stations implies that a specific city area is temporarily unaccessible. To quantitatively evaluate the severity of this issue, we introduced a measure denoted as criticality. This measure counts the number of recorded timestamps (i.e., the number of dataset records) at which all the stations of the considered OMP have a critical level of occupancy. Intermittent situations are potentially harmful as well because the stations in the group are overloaded in an alternate fashion. While considering nearby stations, some free docks are available in the corresponding area, but a potential service disruption may occur when a user arrives at an overloaded station. Still, the user could reach any of the close stations, since some of them are underutilized. To quantitatively estimate the severity of an intermittent situation, we introduced the intermittence measure. Intermittence counts the number of points of time at which at least one station (but not all of them) of the considered OMP has an occupancy level above a given threshold. The higher the intermittence, the more severe the imbalance situation. More formal definitions of the OMP and its quality measures follow. **Definition 2** (Occupancy Monitoring Pattern). : _Let \(\mathcal{D}\) be an occupancy level dataset and let \(\mathcal{S}\) be its attribute set. An Occupancy Monitoring Pattern (OMP) \(P\) in \(\mathcal{D}\) is a set of \(k\) distinct stations in \(\mathcal{S}\), i.e., \(P=\{s_{1},\,\ldots,\,s_{k}\}\), \(s_{i}\in\mathcal{S}\)._  
**Definition 3** (Criticality measure). : _The criticality of an OMP \(P\) in dataset \(\mathcal{D}\) indicates the number of records \(R_{i}\) in \(\mathcal{D}\) for which all the stations in \(P\) take value Overloaded. It is defined as the number of \(R_{i}\) in \(\mathcal{D}\) such that \(\forall\ (s_{j},o_{i}^{j})\in R_{i}\) the following conditions hold: (i) \(s_{j}\in P\); (ii) \(o_{i}^{j}=\text{Overloaded}\)._  
The criticality values of similar OMPs are correlated with each other.