# A Lifetime Maximization Relay Selection Scheme in Wireless Body Area Networks
## 6 Performance Evaluation
### Result Analysis
Using multi-hop transmission can effectively reduce transmission distance, resulting in energy cost decrease. While in WBANs, energy depletion of a sensor node reduced by two-hop transmission is smaller than extra costs for relay nodes. That is to say, when using benchmark strategy, the total consumption of the network is the minimum. As a result, the relay selection scheme obtained from the sum-rate algorithm is consistent with benchmark strategy. Another observation is that when \(\sigma^{2}=0\), the performance of the maxi-rate algorithm is the same with LMRSS and gradually falls behind with the increasing \(\sigma^{2}\). This is because when all the sensor nodes have the same amount of energy, minimizing the maximum consumption rate is equivalent to maximizing the minimum lifetime among nodes. When energy difference degree becomes larger, only pursuing to minimize the consumption rate regardless of residual energy of sensor nodes may lead to allocating too much relay burden on a relay node, which relatively lacks residual energy and consequently hinders the enhancement of network lifetime. Figure 4 shows the averaged sum of energy consumption rates of sensor nodes in one superframe under different relay selection algorithms in the simulation. It can be seen that the sum-rate algorithm together with benchmark spends the least because of its optimization objective. LMRSS consumes 13% and 5% more energy than the sum-rate algorithm and maxi-rate algorithm, respectively. It is inferred from the figure that the sum-rate scheme realizes the best energy efficiency, which is the minimum sum of energy consumption rate of all of the sensor nodes in the network, but it does not get the best performance of enhancing network lifetime. Hence, just concentrating on network level energy efficiency is not an appropriate way to prolong network lifetime, as shown in Figure 3. More specifically, in the environment of WBANs, where lifetime may be more important than energy efficiency, LMRSS results in a slight drop in energy efficiency; however, it produces more considerable improvement of network lifetime. In addition to the explanation for the impact of energy consumption and energy storage of sensor nodes on network lifetime performance, we analyze the worst case for relay selection where sensor nodes in the main body part possess less energy than other nodes in the rest parts. That is, relay nodes are short of energy more seriously than faraway sensor nodes. In this case, LMRSS is out of action since it aims to protect relay nodes that are more energy-restrictive and may run out of energy first. In order to prolong the lifetime of relay nodes, LMRSS will not allocate faraway sensor nodes to any relay nodes so as to cut down on the energy depletion of relay nodes. As a consequence, LMRSS is equal to the direct transmission strategy in this case. On the contrary, the maxi-rate algorithm focuses only on energy consumption of WBANs, and it will still allocate faraway sensor nodes to energy-restrictive relay nodes to achieve its target on energy consumption rate. As a result, relay nodes will accelerate to exhaustion, which, in turn, degrades the network lifetime performance of WBANs. Table 4 shows the network performances of different relay selection methods in the worst case via simulations to validate  
Figure 4: Energy consumption performance comparison. our analysis above. We set residual energy in sensor nodes belonging to the main body part as 1 J and as 2 J for the other sensor nodes in the network to simulate the worst case in relay selection. As shown in the table, for the maxi-rate algorithm, the maximum consumption rate of sensor nodes within the networks is the lowest. However, its network lifetime performance is decreased by 30% compared with the benchmark strategy since the maxi-rate algorithm only focuses on the energy consumption criterion and neglect energy storage of each sensor node. Meanwhile, as discussed before, LMRSS in this case selects to use direct transmission only, which is the same with benchmark strategy.