# Novel Reliable and Energy-Efficient Routing Protocols for Wireless Sensor Networks
## 6 Simulation Results
Figure 5 shows the success probability with OREBP and PEGASIS. We assume a predefined data loss rate \((\varepsilon=0.05)\) for OREBP. The success probability for PEGASIS is calculated as mentioned above. The figure shows the success probability against a variable number of hops ranging from one to six. OREBP always has a higher success probability than PEGASIS, although the value depends on the number of hops. The figure shows that using OREBP improves the reliability from 63% in case of a one-hop path to 71% in case of a six-hop path. Lost data means wasted energy. The figure shows that the success probability decreases with an increasing number of hops. In OREBP, we can control the success probability by trading off between predefined data loss \((\varepsilon)\) with life span, as shown in Figure 4.  
Figure 6 shows the relationship between the life span and the number of hops with MMREP, OREBP, and PEGASIS. We assume a predefined data loss rate (\(\varepsilon=0.05\)). In the case of MMREP, OREBP, the consumed energy depends on \(\varepsilon\). The probability of the overall success of packet transmission from the source node to the BS should satisfy \(\Pi_{j=0}^{m}P_{l_{j}l_{j+1}^{n}}=1-\varepsilon\), where \(m\) is the number of the hops. The figure shows the life span against a variable number of hops ranging from one to four. We note that the life span with OREBP increases as the number of hops increases. But, in the case of MMREP, the relationship is unstable because the set of Equations (11) is solved num  
Figure 4: Life span with different data loss \((\varepsilon)\). Figure 5: Success probability when data loss \((\varepsilon=0.05)\). solutions are found, so, one needs an algorithm to pick the suitable solution. In OREBP, life span increases as the number of maximum hops increases because there are more paths available to select from. With PEGASIS, the consumed energy is a function of single transmissions rather than the path overall transmissions, so it does not depend on the number of hops. As the number of hops increases, not only the life span increases, but also the complexity of the algorithm increases. Figure 7 shows the relationship among the maximum number of hops \(m\), on the \(x\)-axis, the life span \(y\)-axis on the left, and the execution time (a proxy for the complexity) on the secondary \(y\)-axis on the right. As expected, the figure shows that in OREBP as the number of hops increases, the life span increases, but the complexity of the protocol also increases. The user has the choice of trade-offs between the life span, the complexity, and the maximum number of hops. All the figures show higher a life span with PEGASIS, but also a high percentage of lost data, which implies wasted energy. The results show that the performance of OREBP is better than the performance of MMREP. As we mentioned, MMREP is the basic idea of the algorithm, but we used the entropy principle to optimize it and to reduce its complexity. Figure 6: Life span and maximum number of hops (\(\varepsilon=0.05\)). Figure 7: Life span, number of hops, and execution time.