## 3 Results  
### Examples  
Let us now see two CD examples from the given application field. In these examples, we intend to detect change in the RET based on TS occurrences along a route. The full length of the trip represented in the table is 4.6 km. The TSs are assumed to be detected and located by an on-board TSR system. The TS locations are marked with the corresponding TSs in the top band of Table 2. The sequence given there is synthetic, and has been compiled for the purpose of demonstrating  
* a RET transition from a Dt to a Res area (denoted by Dt \(\rightarrow\) Res), if the virtual journey is taken from the left, and
* a RET transition from a Res to a Dt area (denoted by Res \(\rightarrow\) Dt), if the journey is taken from the right. In the middle and the bottom bands of Table 2, the actual counts of the NS, PL, GW, and SL TSs for the virtual trips starting from the left, and from the right, respectively, are given. These counts have been produced in a unified and generic manner, i.e., without demarking the validity intervals of the respective counting measures. As these counts are denoted simply by \(N^{NS}\), \(N^{PL}\), \(N^{GW}\), and \(N^{SL}\) in the present and in the subsequent subsections, care should be taken to use them properly, i.e., according to the direction of the virtual trip. In the sequence given in the top band, each \"--\" signifies a 0.2 km path-length along the route without any relevant TSs--facing the ego-car--installed/detected along the corresponding patch of road. It should be underlined that these fixed path-length route-segments are used in the examples simply for convenience, i.e., to make diagrammatic representation of the TS sequence, as well as the virtual trip easier to follow, and to make the calculations and diagrams easier to verify. In each of the two examples that are presented in this subsection, the specific PHCD is applied to a RET transition that is homologous to the one, the PHCD has been tuned to. First, let the ego-car start its virtual trip from the left. This case is described in detail in Example No. 1. 3.1.1 Example No. 1: A Dt \(\rightarrow\) Res Change Detector Applied to a Homologous RET Transition  
In the TS sequence given in the top band of Table 2, the intended RET transition (i.e., the Dt \(\rightarrow\) Res) occurs at about the path-length of 2.2 km (i.e., having covered eleven dashes from the left in the band). The presence of such a RET transition in the synthetic sequence was secured by having inserted into it five TSs that are more characteristic of the Res areas than of the Dt areas--see the rightmost column of Table 1--in consecution and reasonably close to each other starting from this path-length along the virtual route. According to the CUSUM-based RET CD method derived in Section 2.2, functions \(g_{T}\) and \(h_{T}\) are to be used for the purpose of CD. These functions are now denoted by \(g_{I}^{Dt\to Res}\) and \(h_{I}^{Dt\to Res}\), respectively. The lower and upper indices indicate the function's dependence on path-length \(l\) and the RET transition actually monitored by the change detector, respectively. These functions are given in Equations (12) and (13), respectively. In the former, the coefficients are given with the same numerical precision as was used in Table 1.  
\[ \begin{array}{ll}g_{I}^{Dt\to Res}\approx&2.80\ \text{km}^{-1}\cdot l-1.74 \cdot N^{NS}(l)-\\ &-1.92\cdot N^{PL}(l)+0.13\cdot N^{GW}(l)+0.69\cdot N^{SL}(l)\end{array}  \tag{12}\]  
\[ \begin{array}{ll}h_{I}^{Dt\to Res}=g_{I}^{Dt\to Res}-\inf_{s\leq l}g_{s}^{ Dt\to Res}.\end{array}  \tag{13}\]  
For the generation of these functions, the actual counts of the four considered TS types--at a particular path-length--are required. These counts are given in the middle band of Table 2 for virtual trips starting from the left.