## 6 Simulation  
This section presents the simulation study of our data-centric strategy in specific scenarios. We perform our evaluation by using the NS-2 (Network Simulator 2), version 2.33 ([[http://nsnam.isi.edu/nsnam/index.php/Main_Page](http://nsnam.isi.edu/nsnam/index.php/Main_Page)]([http://nsnam.isi.edu/nsnam/index.php/Main_Page](http://nsnam.isi.edu/nsnam/index.php/Main_Page))). Each simulated scenario was executed with \(33\) random topologies. At the end, for each scenario we plot mean values with \(95\%\) (symmetric asymptotic) confidence intervals.  
To identify assess the network behavior, we variate the number of nodes and the stream size (\(|\mathbf{V}|\)). The evaluated parameters are the delay and error in data quality, specified by two statistical tests. The default parameters used in simulations are presented in Table 1.  
To evaluate the delay in real-time scenarios, it is important to determine the minimum deadline (\(d_{min}\)) for each number of nodes and \(|\mathbf{V}|\) being considered. To do this, we consider different network sizes (\(128\), \(256\), \(512\), and \(1024\)), the \(|\mathbf{V}|=\{256,512,1024,2048\}\), and only one data source generating \(\mathbf{V}\). In our case, the \(d_{min}\) values is determined by measuring the time between the first data packet sent by the source and the last packet received by the sink, _i.e._, the time for \(\mathbf{V}\) to be entirely received by the sink. Figure 4 illustrates \(d_{min}\) values for all scenarios being considered.  
It is important to highlight that if either application has a deadline smaller than the one shown in Figure 4 or the network is not in perfect conditions, then all data cannot be transmitted unless some reduction is performed. However, despite all nodes (sources) know the real time requirements of the packets they generate, they cannot infer the necessary data reduction locally because the network has some global restriction not perceived for them.  
In the problem scope defined in Section 2., we discuss the impact of the solutions regarding the data quality, which is considered as our decision \(D\). To assess the impact of data reduction on data quality,  
\begin{table}
\begin{tabular}{l c} \hline
**Parameter** & **Values** \\ \hline \hline Network size & Varied with density \\ Queue size & Varied with stream \\ Simulation time (seconds) & \(1100\) \\ Stream periodicity (seconds) & \(10\) \\ Radio range (meters) & \(50\) \\ Bandwidth (kbps) & \(250\) \\ Initial energy (Joules) & \(1000\) \\ \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
Figure 4: Minimum deadlines.  
based on decision \(D\), we consider the rules \(R_{dst}\) and \(R_{val}\) defined before. These rules are represented by \(\Upsilon\) and \(\Phi\) errors, respectively.  
It is possible to apply these rules, because we consider the reduction of only one source, _i.e._, our sampling is performed in each data set separately. For example, considering a simple network of nodes connected as a tree as _Sink-Node\({}_{A}\)-Node\({}_{B}\)_. After in network data reduction we give equal opportunity to the data points of _Node\({}_{A}\)_ and _Node\({}_{B}\)_ separately. So, clearly the data gathered in the sink will represent the original data of the network, where neither data nodes will be over-represented.  
The deadlines for the real-time scenarios, that we consider, are \(50\%\) of the minimum deadlines with(out) concurrent traffic; minimum deadlines with delay caused by relay nodes in each packet transmitted with(out) concurrent traffic. These study are discussed in the next subsections. For all scenarios, we evaluate the simplified and complex formulations, both using \(\Psi_{\mathrm{central}}\) or \(\Psi_{\mathrm{random}}\). We use a Monte Carlo simulation [41] considering a complete mapping between the number of nodes and the stream size, only unusual results will be presented. However, the y-axis scale is not kept constant in all figures. The reason is that such a re-scale allow us to make better analysis.