## 7 Performance Evaluation and Analysis  
In this section, we study the performance of 4-chain, 2-chain, single-chain, PEGASIS [12] and C-PEGASIS [14] routing schemes in realistic acoustic environment. Loss caused by shipping, thermal and turbulence noise is also computed. In simulations, we have assumed a cylindrical network of area 10,000 \(m^{2}\) with the sink stationed at one end of the network. There are 100 sensor nodes randomly deployed in the network. Each sensor node has a transmission range of 250 m. By following the convention of existing routing protocols of UWSNs, we use an acoustic modem of LinkQuest UWM1000 [32] having a bit rate of 10 kbps. Sensor nodes transmit a data packet after every 16 s. According to the specifications of the modem, the power consumption in transmission, reception, and  
Figure 7: Single-chain based routing. idle mode is 2 W, 0.1 W, and 10 mW, respectively. The size of the data packet and control packet is 50 bytes and 8 bytes, respectively. The initial energy of the sensor node is set as 10 joules. Figure 8 shows that the network lifetime of the single-chain based scheme is much smaller than that of the other two schemes. In single-chain routing, there is large forwarding burden on the single chain head; however, in the other two schemes, the load is divided among two or four chain heads. Although residual energy is also among the factor which is used in the selection of chain head, it does not improve the network lifetime in single-chain as in the 2-chain and 4-chain based routing schemes. In 4-chain routing, network lifetime is higher than 2-chain based routing scheme. This is because of more chain heads in 4-chain based scheme than in 2-chain based scheme. The problems of the presence of distant neighbor and _long link_ are very important in chain-based routing. In the multi-chain based routing, these problems are removed by using the interconnection between the chains. Nodes having distant neighbors are connected to their nearest neighbor in any other chain. In PEGASIS, quick death of nodes in the early time duration causes a shorter stability period. The chain head having larger distance from the sink than the other nodes consumes a large amount of energy in data aggregation and transmission. Moreover, there is a trade-off between the stability period and network lifetime. Therefore, PEGASIS has a longer lifetime than single-chain based routing; however, it has smaller stability period than the later scheme. The nodes nearer to the sink remain alive for a longer duration than the other nodes. Congestion consideration in C-PEGASIS prolongs its stability period and network lifetime to some extent (_i.e._, better than PEGASIS and single chain); however, this impact is less than that of the 2-chain based and the 4-chain based schemes. Figure 9 shows the comparison of average end-to-end delay between the 4-chain, the 2-chain, the single-chain, PEGASIS, and C-PEGASIS. In this figure, we see that the aggregated delay of single chain based scheme is much higher than the other two schemes as all children nodes of the single chain have to forward their data through the same central path. Large transmission distance causes high propagation  
Figure 8: Number of dead nodes in 4-chain, 2-chain, single chain-based routing and PEGASIS. delay between the end nodes of the chain and the chain head. Nodal delay decreases with the decrease in the number of nodes. Nodal delay is the time taken by a node in data processing. Multi-chain schemes have low end-to-end delay as, if their parent node dies, the distant nodes forward their data to the nearest nodes of the interconnected chains. It reduces the burden on distant forwarder nodes in the same change. It also minimizes the propagation delay of the network. In PEGASIS, the sharp variations in delay are due to the formation of the chain head at different locations. Aggregated network delay falls due to quick death of distant nodes from the sink.