## 3 Results
### Further Examples  
In each of the two examples below, an \"off-the-tune\" RET change detector is considered. These change detectors are applied to the TS sequence used above, furthermore, the same marked Poisson process reference parameters are used. The examples below demonstrate that \"off-the-tune\" change detectors may behave fairly haphazardly. In [17], approaches are proposed to deal with such behavior of the change detectors. These approaches are essential if several differently tuned change detectors are to be used within a compound system, e.g., for the purpose of RET detection and identification, rather than CD.  
2.1 Example No. 3: A \(\mathrm{Res}\rightarrow\mathrm{Dt}\) Change Detector Applied to a \(\mathrm{Dt}\rightarrow\mathrm{Res}\) Transition  
Functions \(g^{Res\to Dt}_{l}\) and \(h^{Res\to Dt}_{l}\) to be used for signaling a RET transition \(\mathrm{Res}\rightarrow\mathrm{Dt}\) have already been presented--in conjunction with the Example No. 2--in Equations (14) and (15), respectively. The only difference is that now we need to use these functions with the TS counts given in the middle band of Table 2, rather than with the TS counts given in the bottom band, as the car is now driven from the left to the right (i.e., a Dt \(\rightarrow\) Res transition is expected).  
In Figure 3, the diagrams of \(g_{\to l}^{Res\to Dt}\) and \(h_{\to l}^{Res\to Dt}\) are shown for an intended RET transition Dt \(\rightarrow\) Res, respectively. The detector takes the first 0.8 km starting from the left for a Res area and then detects a change Res \(\rightarrow\) Dt at that point (e.g., with a threshold \(\delta=1.0\)). If threshold \(\delta=3.0\) is used instead, then the RET transition will be detected at 1.0 km. The corresponding detection lags for these two thresholds are 0.8 and 1.0 km, respectively. If we use larger thresholds, say, \(\delta=4.0\), or \(\delta=5.0\), then for the former, an extra detection lag of 0.9 km will be introduced, while the latter will completely miss the Dt segment of the route.  
The intended RET change of transition Dt \(\rightarrow\) Res remains undetected by this detector no matter what \(\delta>0\) is used.  
2.2 Example No. 4: A Dt \(\rightarrow\) Res Change Detector Applied to a Res \(\rightarrow\) Dt Transition  
In Figure 4, the diagram of function \(g_{l\gets l}^{Dt\to Res}\) is shown for the intended RET transition Res \(\rightarrow\) Dt. This transition is present when driving from the right along the considered TS sequence. Note that for the given TS sequence and for the given process parameters, functions \(g_{l\gets l}^{Dt\to Res}\) and \(h_{l\gets l}^{Dt\to Res}\) happen to be identical. Using threshold \(\delta=3.0\), the detector signals a change Dt \(\rightarrow\) Res at about the path-length of 1 km.  
Figure 4: Function \(g_{l\gets l}^{Dt\to Res}\) for the considered TS sequence. For the given sequence and for the given process parameters functions \(g_{l\gets l}^{Dt\to Res}\) and \(h_{l\gets l}^{Dt\to Res}\) happen to be identical.  
Figure 3: A Res \(\rightarrow\) Dt change detector applied to a Dt \(\rightarrow\) Res transition showing up in the TS sequence given in the top band of Table 2: (**a**) Function \(g_{\to l}^{Res\to Dt}\) for the considered TS sequence and (**b**) Function \(h_{\to l}^{Res\to Dt}\).