## 6 Simulation
### Delay Caused by Relay Nodes with Concurrent Traffic  
The last scenario considers \(d_{a}=d_{min}\), concurrent traffic, and all relay nodes delay the stream fragments at \(0.01\%\) of the \(d_{a}\). Again, we use a \(128\)-node network and vary the percentage of nodes generating traffic (\(16\%\), \(20\%\), \(25\%\), and \(33\%\) of \(128\) nodes) and \(|\mathbf{V}|\) (\(256\), \(512\), \(1024\), and \(2048\)). The  
Figure 12: \(\boldsymbol{\Upsilon}\)-error considering the half of deadlines with concurrent traffic.  
Figure 13: \(\boldsymbol{\Phi}\)-error considering the half of deadlines with concurrent traffic.  
objective of this scenario is to identify the best strategy when the relay nodes have extra tasks with high priority and the network has a traffic that gradually increases.  
Figure 14 shows the delay results in a \(128\)-node network varying the percentage of nodes generating traffic and \(|\mathbf{V}|=2048\). The \(d_{a}\) is met in most cases. The complex formulation presents a more scalable behavior considering the percentage of nodes generating data. This occurs because the \(\mathbf{\Psi}\)-reduction estimation [Equation 7] is related to \(d_{a}\), _i.e._, if \(d_{a}\geq d_{min}\) the \(\mathbf{\Psi}\)-reduction cannot be efficient, when we consider other delay aspects, like concurrent traffic.  
Figures 15 and 16 show the error evaluations considering a network with \(128\)-nodes, varying the percentage of nodes generating traffic and \(|\mathbf{V}|=256\). Simplified and complex formulation are presented by using \(\mathbf{\Psi}_{\mathrm{central}}\) and \(\mathbf{\Psi}_{\mathrm{random}}\). Figure 15 shows that in all cases we have \(\mathbf{\Upsilon}\leq 40\%\). The \(\mathbf{\Psi}_{\mathrm{central}}\), in  
Figure 14: Delay considering the delay caused by relay nodes with concurrent traffic.  
Figure 15: \(\Upsilon\)-error considering the delay caused by relay nodes with concurrent traffic.  
complex formulation, has a smaller \(\Upsilon\)-error. The reason is that the complex formulation performs the maximum \(\mathbf{\Psi}\)-reduction sooner (\(\mathbf{\Psi}_{\mathrm{central}}\) is executed once or twice). This result shows that because fewer successive \(\mathbf{\Psi}\)-reductions are performed, more representativeness is kept in the reduced data, _i.e._, data degradation is mitigated.  
Figure 16 shows that, in general, we have \(\mathbf{\Phi}\leq 30\%\). The complex formulation with \(\mathbf{\Psi}_{\mathrm{central}}\) presents \(\mathbf{\Phi}\approx 5\%\). The reason is that the \(\mathbf{\Psi}_{\mathrm{central}}\) has a smaller \(\mathbf{\Phi}\)-error because the central elements choice improves the average test and the complex formulation performs the maximum \(\mathbf{\Psi}\)-reduction early.  
The errors evaluation suggest that the complex formulation is more appropriate with the \(\mathbf{\Psi}_{\mathrm{central}}\) strategy. The partial conclusion, considering this scenario, is that the complex formulation is actually more appropriate, because the deadlines are met in all cases while keeping data representativeness. Considering the sampling algorithm, the \(\mathbf{\Psi}_{\mathrm{central}}\) strategy with complex formulation is always indicated.