# Novel Reliable and Energy-Efficient Routing Protocols for Wireless Sensor Networks
## 6 Simulation Results  
The performance of the proposed algorithms MMREP and OREBP, respectively are evaluated in comparison to the PEGASIS protocol. In PEGASIS, each node forwards the packet to its closest neighbor; when the packet arrives at the chain leader, it sends the packet directly to the base station. PEGASIS does not take reliability into consideration, whereas MMREP and OREBP do. To introduce reliability constraints to PEGASIS and thus make it comparable with the proposed protocols, it is modified as follows: each packet should be forwarded to the BS with at least success probability \(Pij=(1-\varepsilon)\), where \(i\) is the source node and \(j\) is the destination node. From Equation (1) \(P_{ij}=\exp\left(a_{ij}^{a}\frac{\theta a_{2}^{2}}{\beta i_{j}}\right)\), \(g_{ij}\) is calculated as in [26]. In case of an \(m\)-hop path, \(P(path)=\sqrt[n]{1-\varepsilon}\). For the whole round, we will calculate the average success probability of all paths. Figure 1 shows how 100 nodes are deployed randomly onto a grid of 100 m \(\times\) 100 m according to a 2D normal distribution; the BS is allocated in the upper-right corner of the sensing field, as shown by the green point. while Figure 2 shows the network as a graph. The highlighted chain is constructed by the Dijkstra shortest path algorithm, as defined by the base station. The transmission energy will be calculated according to the Rayleigh fading model (1) under the following assumptions:  
Figure 1: Simulated network. Figure 2: The network as a graph. We neglect the conditioning energy needed by the electronics. * \(\theta=10^{-6}\)
* \(\sigma_{Z}^{2}=0.1\)
* \(\alpha=2\)
* \(P_{ij}\) is calculated based on reliability \((1-\varepsilon)\) and the number of relay nodes \(m\), where \(\Pi_{j=0}^{m}P_{l|j_{j+1}}\geq 1-\varepsilon\). We assume that \(P_{ij}\) is the same for all nodes, then \(P_{ij}=\sqrt[n]{1-\varepsilon}\). * All the nodes have the same initial energy. * The life span is the number of packets transmitted over the chain until the first node goes flat. Each transmission round carries a single packet. * Each node has an adjustable power transmission, which enables it to access any node in the chain including the BS. The path shown in Figure 2 consists of seven nodes, numbered from 1 to 7, where node number 1 is the farthest from the BS, it shown as red point in Figure 1. Figure 3 shows the residual energy of the nodes of the chain for MMREP, OREBP, and PEGASIS respectively, when the first node goes flat. In the case of MMREP and OREBP, we note that almost all the nodes have the same level of residual energy, the residual energy is distributed more uniformly (near zero) for all nodes, In the case of PEGASIS, we note that as the node gets further away from the BS, it loses energy at a higher rate, the residual energy of the nodes decreases as the nodes gets farther from the BS. So, we note unevenly distribution of the residual energy. Figure 4 shows the life span of a network which uses MMREP, OREBP, PEGASIS, subject to a reliability constraint, with different data loss percentage \(\varepsilon\) values, 0.025, 0.05, 0.075, 0.01, 0.125 and 0.15, respectively. Since PEGASIS does not consider \(\varepsilon\) when calculating transmission energy, the figure shows that it has a higher life span than MMREP and OREBP; it uses lower transmission energy, which causes a higher packet loss percentage, which means lower reliability; hence, the life span of a network with PEGASIS is the same regardless of data loss percentage \(\varepsilon\). In the case of the proposed algorithms, however, life span increases with increasing data loss percentage \(\varepsilon\), while the probability of successful packet transmission (1-\(\varepsilon\)) is decreasing. With MMREP and OREBP, the life span is a function of \(\varepsilon\). The users can trade-off between the reliability represented by \(\varepsilon\) and the life span. Figure 3: Distribution of residual energy on the path at the moment when the first node goes flat.