# Buffer with N Policy and Active Management
## 5 Numeric Examples
### Impact of the Threshold Value  
In this section, we investigate how the performance can be controlled by varying the threshold value, \(K\), in two scenarios: when passive management is applied in both phases, and when active management is applied in both phases. In the latter case, we use two mild dropping functions, \(d_{1}(n,3)\) and \(d_{2}(n,3)\). We maintain the buffer size \(N=100\) and vary \(K\) from 1 to 100.  
Figure 11 depicts the energy efficiency versus the threshold \(K\) in both scenarios of interest. In the case of passive management (red line), the energy efficiency changes very little with \(K\), remaining close to 0.5 irrespective of the value of \(K\). This outcome is not surprising, as adjusting \(K\) simply lengthens or shortens both phases proportionally. However, this observation has significant practical implications. In the passive management scenario, the only parameter available to adjust energy efficiency is \(K\), and unfortunately, only minor changes in \(E\) are achievable by manipulating \(K\). In contrast, in the active management scenario (blue line), we can significantly alter energy efficiency solely by adjusting \(K\). In other words, if there is a need to maintain \(d_{1}\) and \(d_{2}\) unchanged while adjusting energy efficiency, \(K\) can be manipulated for this purpose as well.  
In Figure 12, the average queue length versus threshold \(K\) is depicted in both scenarios of interest. As observed, the curve is almost identical and nearly linear in both cases. Thus, the ability to adjust the queue size is similar in both active and passive management approaches.  
Figure 13 depicts the throughput versus the threshold \(K\) in both scenarios of interest. We see that in the case of active management (blue line), the throughput varies significantly with \(K\), allowing us to control the throughput to a large extent, similar to how it was with energy efficiency in Figure 11. Likewise, the red line is almost flat in Figure 13, indicating that in the passive management case, only minor changes in throughput are achievable by adjusting \(K\).  
Figure 10: Cost \(c_{2}\) vs. parameters \(a\) and \(b\) of active management during both phases of operation.  
When comparing Figure 13 with Figure 11, we also observe that in the active management case, better energy efficiency results in worse throughput, and vice versa. This is a clear consequence of the policy design, i.e., it is not possible to achieve both very high throughput and very low energy consumption simultaneously. The main advantage of active management, as applied here, is that we can adjust one of these characteristics to suit our needs, perhaps at the cost of the other. Such adjustment is hardly possible in the case of passive management, as the red lines in Figures 11 and 13 are practically flat.  
Figure 11: Energy efficiency vs. threshold \(K\) in two situations: when passive management is applied in both phases (red curve) and when active management is applied in both phases (blue curve).  
Figure 12: Average queue size vs. threshold \(K\) in two situations: when passive management is applied in both phases (red curve) and when active management is applied in both phases (blue curve).  
Figure 13: Throughput vs. threshold \(K\) in two situations: when passive management is applied in both phases (red curve) and when active management is applied in both phases (blue curve).