## 7 Results and Performance Evaluation
### Evaluation of Base Station-Centric (Centralized) Versus Node-Centric (Decentralized) Approaches
#### 7.6.1 Communication Energy Efficiency  
We assume that the inter-nodal distance (hop distance) between any two nodes is the same.  
Let:  
\(e\) be the energy in joules required for transmission of one packet over one hop, and  
\(h\) be the number of hops between a typical node to the base station.  
In the proposed system, the node transmits only one additional packet containing its RSS value to the base station. If the nodes communicate frequently with the base station (sink) in the normal traffic pattern, the jamming-related data (the RSS packet) can be piggybacked with this traffic reducing the overhead. If, however, the normal traffic is very low, then the packet has to be sent independently which will increase the overhead. We will consider the latter case (the worse case). Let \(f\) be the number of such jamming-related data (the RSS packet) being sent by a typical node to the base station (sink) per second. Therefore, the total energy consumed per second for communication in the proposed centralized system, _Ec-cent_ in joules is:  
\[\textit{Ec-cent}=\textit{efh} \tag{11}\]  
Under the existing approaches (the decentralized approaches), e.g., in the models suggested by [PERSON] _et al._[1], [PERSON] _et al._[2], and [PERSON] _et al._[3], the nodes have to communicate with their neighbors for neighborhood check or for sampling and threshold fixing. In these approaches, if a node has \(n\) neighbors, it has to send minimum one packet to each neighbor and receive one packet from each neighbor for neighborhood check. Let the frequency of this neighborhood-check (or, the number of time-windows during which metric-samples from neighbors are to be collected per second, as done in some cases, be \(t\) (_t_ may be less than 1). Therefore, the minimum number of packets exchanged per hop per suspected jamming attack is _2 nt_. If \(j\) is the average number of suspected jamming attacks per second, then the energy required for communication with the neighbors is _2 ntej_ joules per second. The nodes under the decentralized approach are then required to communicate to the base station if they detect jamming. Assuming that a fraction \(k\) of the \(j\) suspected jamming attacks are detected to be actual jamming, the node has to communicate _kj_ times per second with the base station. Assuming further that the node sends only one packet per such communication, the energy required for this communication is _ejkh_ joules per second. We thus have the total energy required for communication under the decentralized system in joules per second, _Ec-decent_ given as:  
\[\textit{Ec-decent}=\textit{2 ntej}+\textit{ejkh} \tag{12}\]  
For our proposed (centralized) system to be more communication energy efficient than the existing (decentralized) approaches, _Ec-cent_ must be less than _Ec-decent_, _i.e._,  
\[\textit{efh}<\textit{2 ntej}+\textit{ejkh} \tag{13}\]  
\[\textit{or},\textit{f}<\textit{j(2 nte/h}+\textit{k)} \tag{14}\]  
Therefore, as evident from Inequality 14, our method (the centralized approach) can be only conditionally more communication energy-efficient than the existing (decentralized) approaches. It can thus be concluded that whether a distributed or centralized approach is more communication energy efficient depends on the communication pattern of the application.