## 6 Performance Evaluations
### Analysis of Results  
Simulation experiments were performed to verify the correctness of operations, and evaluate the performance of the proposed framework and network protocol. The simulator is event-driven and it was written using Java. It places all the nodes in a linear formation, and simulates the communication and routing processes as described in the paper. The main focus of the experiments was to validate and evaluate the design and inter-workings of the proposed model. The simulator was designed and tested according to the model and structure presented in [36]. As indicated in Table 1, the number of DDN nodes used in the simulation is 10, the number of DRN nodes per DDN node was varied between 25, 50, 100, and 150. The number of BSN nodes per DRN node is 6. DRN nodes communicate using a data rate of 4,800 bps. Depending on the transmission range of the nodes, this number of nodes covers an area of tens of kilometers while the network can cover longer stretches of pipelines. However, since the hierarchical network consists of segments which are separated by the DDN nodes, the simulation of several segments of the network is relatively sufficient to reflect the performance of the entire system. This is because the data is only multi-hopped through the DRN nodes to the nearest DDN node. The data is then transmitted by the various DDN nodes to the NCC in parallel. In the simulation,the BSN nodes send their sensed data to their parent DRN node in a periodic manner. The sensing period that was used in the simulation is 10 seconds. This value may be varied depending on the requirements of the application used and the type of parameters sensed. After collecting the information from the BSN nodes, the DRN nodes use the networking protocol to route this information to their parent DRN node. The DRN data packet size was set to 512 bytes, which is a common size and it is sufficient to include the sensed information. For the SRJ algorithm the MAX_JUMP_FACTOR is set to 3. We believe that this is a reasonable value to overcome 3 consecutive node failures by increasing the DRN node transmission range accordingly. To verify and test our RA, and SRJ routing protocols and their ability to route the generated packets correctly to the DDN nodes using intermediate DRN nodes, a number of DRN failures have been intentionally generated using the Poisson arrival distribution with certain average arrival rate. The average arrival rate of the DRN failures varied from 0 to 4.5 percent of the total number of nodes per month. For example, if the number of DDN nodes is 10, and the number of DRNs per DDN nodes is 100, then the total number of DRN nodes is 1,000. At an average failure rate of three percent per month, the actual number of additional failed nodes for each month is 3% of 1,000 which is 30 nodes. The simulation is designed to evaluate the capability of the routing protocol to overcome intermediate DDN node failures. The failure rate range that is used in these experiments is only theoretical, and is intended to compare the ability of the introduced linear routing protocols to overcome possible node failures. The actual failure rate would be dependent on the application, geographic location, environmental conditions, and specific type and reliability of the devices that are used as DRN nodes as well as the expected device lifetime in the particular environment where the nodes are deployed. The failures may be due to external factors imposed by the physical environmental elements or by internal factors such as hardware or software malfunction due to aging or manufacturing defects. The total simulated time was 20 months. The results for underwater acoustic wireless sensor networks are presented in the Figures 11-14. As DRNs fail, routing of the DRN packets to either the parent DDN or the alternative one in the opposite direction is done. In Figures 11-14, the number of DRNs per DDN was varied in order to study the impact of increasing the number of DRNs per DDN on network performance.