# A Mobility-Aware Adaptive Duty Cycling Mechanism for Tracking Objects during Tunnel Excavation
## 4 Analysis and Evaluation
### Evaluation in Tunnel Excavation  
To compare the proposed mobility-aware adaptive duty cycling mechanism and the periodic one, we simulated a dump truck that transfers excavated material out of the tunnel. During the mucking process, an empty dump truck goes into the tunnel, approaches the payloader working at the blind side, stops for loading, and then comes out of the tunnel. The dump truck typically moves inside the tunnel excavation site at the speed of 30 km/h, and it takes about 10 minutes to load a truck.  
For the simulation analysis, we used \(\alpha=2\), \(\beta=2\), \(D=1\%\), \(T=50\) ms, and \(P_{W}=58\) mJ/s. For evaluation of the proposed adaptive duty cycling mechanism, it was assumed that the condition of \(\Delta RSSI>\lambda\) is always satisfied while the truck is moving, and the condition of \(\Delta RSSI<\lambda\) is always satisfied while the truck is stopped. Accordingly, the sleep time is halved while the truck is moving, and is doubled while the truck is stopped for the loading. For the periodic mechanism, the sleep time is not adjusted.  
Figure 10 shows the energy consumed by the sensor tagged on the truck as the length of the tunnel excavation increases. With the given analysis condition, the proposed mobility-aware adaptive duty cycling mechanism consumes less energy than that of the periodic, until the length of the excavated tunnel reaches at 1268 m, in which case the probability is 33.7%. This probability is computed by dividing the truck moving time by the total staying time in the tunnel and corresponds to the value obtained from Equation (6). For the tunnel length \(L_{Ttunnel}\), the probability that the proposed mechanism consumes less energy than the periodic one can be computed as:  
\[\begin{array}{ccc}p=\frac{T_{M}}{T_{M}+T_{S}}&\leq&\frac{(\alpha D+1-D)( \beta-1)}{\alpha\beta-1}\\ \frac{2\cdot\frac{L_{Ttunnel}}{T_{M}}}{2\cdot\frac{L_{Ttunnel}}{T_{M}+T_{S}}} &\leq&\frac{(\alpha D+1-D)(\beta-1)}{\alpha\beta-1}\\ L_{Ttunnel}&\leq&\frac{v_{M}\cdot T_{S}\cdot(\alpha D+1-D)(\beta-1)}{2\{\alpha \beta-1-(\alpha D+1-D)(\beta-1)\}}\end{array} \tag{9}\]  
where \(T_{M}\) is the duration of the truck moving, \(T_{S}\) is the stopped time and \(v_{M}\) is the velocity of the moving truck. Note that the excavation face is getting farther away from the tunnel entrance as the tunnel excavation progressed, so the travel distance of the dump truck gets longer. Accordingly, for the proposed adaptive mechanism, the number of duty cycles that use \(\tau/\alpha\) increases with the excavated tunnel length. As a result, the energy consumption increases faster than for the periodic case, which uses \(\tau\).  
Figure 10: Energy consumption and the probability of \(\Delta RSSI>\lambda\) with excavated tunnel length.  
The latency of the two mechanisms was also analyzed with the given analysis conditions. The latency of the proposed adaptive mechanism was 1.23 s and 4.90 s while the truck is moving and stopped for the loading, respectively. For the periodic mechanism, the latency is 2.45 s regardless of the condition of truck movement. Recall that the purpose of this study is to enhance the safety at a tunnel excavation site by tracking moving objects. Considering this, the proposed adaptive duty cycling mechanism provides an advantage over the periodic mechanism and also consumes less energy than the periodic one does. Besides, if the tunnel is excavated from both ends, which is typical, the proposed mechanism can be applied to tunnels with length of about 2.5 km.  
The trade-off between reduction in energy consumed and reduction of latency is a fundamental issue in the design of duty cycling. The proposed mobility-aware duty cycling mechanism is also not free from this issue. By using various values of the sleep time adjusting factors, \(\alpha\) and \(\beta\), an engineer can manipulate the energy consumption per unit time or the latency that meets the specific requirements for a particular tunnel construction site.