## 4 Performance Evaluation  
To validate the performance of our data delivery mechanism in the collection subsystem, we compare the performances of our method with those of Fully Connected NN, (FCNN [14]) and the conventional method. In the conventional method, only one out of the four inputs is used in computing the cost function, _i.e._, f(\(x_{1}\)), f(\(x_{2}\)), f(\(x_{3}\)), and SSR [15]. SSR (Self-Selective Routing) finds the next node with the smallest number of hops to the destination using the lecture hall algorithm originated in the field of NN. SSR uses the hop distance to select the next forwarding node as input metric and then estimates the hop distance from a node to the destination, using NN technique. From the above rationale, SSR is a kind of the conventional method using hop distance in computing the cost function. For the construction of the single-hop collection subsystem, 20 nodes are randomly placed in a 500 m \(\times\) 500 m area. From preliminary experimental results, the optimal learning ratio (\(\eta=0.3\)) is derived to maximize PTSR, as shown in Table 1. Besides, the training time is not issued in the experiments because the NNs are trained within about 5-10 seconds. The training time includes the packet transmission delay and CPU processing time. The link cost function operates in constant time O(1) and repeats n \(\times\)1/\(\eta\) times. Thus, CPU processing time depends on the number of inputs, n. In this case n is only four, which is very small compared to other NN applications with tens or hundreds of inputs. The CPU processing time for training the link cost function is very small which is negligible in our application. We tested our mechanism using the NS-2 simulator. We use the log-normal model to model radio propagation environment. A node sends a HELLO message for every 100 milliseconds. IEEE 802.11 standard is used as the MAC layer. The transmission range of a node is 250 m, and the total simulation time is 360 sec. Each node maintains a single queue of packets from all flows passing through the node. We use an exponentially weighted moving average of the instantaneous queue length as a measure of congestion. The average queue length is updated whenever a packet is inserted into the queue. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(\eta\) & **0.1** & **0.2** & **0.3** & **0.4** & **0.5** & **0.6** & **0.7** & **0.8** & **0.9** & **1.0** \\ \hline PCNN & 0.928 & 0.943 & 0.979 & 0.913 & 0.902 & 0.893 & 0.853 & 0.801 & 0.797 & 0.763 \\ FCNN & 0.757 & 0.769 & 0.792 & 0.749 & 0.744 & 0.734 & 0.706 & 0.660 & 0.611 & 0.599 \\ \hline \end{tabular}
\end{table} 
Table 1: Packet transmission success ratio to determine the optimal learning ratio (\(\eta\)). To analyze the effect of collision on PTSR, we vary the probability of packet collision, using Gaussian distribution with zero mean and standard deviation (\(\sigma_{I}\)) as seen in Figure 5. Methods using the NNs are more robust than the conventional method, irrespective of the degree of packet collision. Method using our method improves the performance compared to the FCNN and the conventional method, by about 22% and 45% respectively. Figure 6 shows the PTSR obtained by varying the QL, using Gaussian distribution and standard deviation (\(\sigma_{2}\)). It shows the effect of network congestion on PTSR. The results indicate that method using our method delivers more packets than the FCNN and the conventional methods, by about 17% and 51%. Figure 7 is the PTSR obtained by varying the RSS in the shadowing propagation model. For varying, we add the log normal random fading with zero mean and standard deviation (\(\sigma_{3}\)). From the figure, we can see that method using our method is more robust despite of dynamic random fading and also improve PTSR (about 23% and 43%), compared to the FCNN and the conventional method. Figure 5: PTSR with varying HMRR using Gaussian distribution with \(N(0,\sigma_{I})\).