# Real-Time Communication Support for Underwater Acoustic Sensor Networks +
## 7 Simulations
### End-To-End Delay Analysis  
In this simulation we also considered the example of Section 5, the topology and delays of Figure 3, and the frame and slot allocations of Table 3. We simulated the network during 30,000 slots, and we assumed a random initial-time (in slots) to start the message transmission. Finally, the set of messages \(m_{ga}\) and \(m_{ag}\) are sent every 100 slots, and the set of messages \(m_{db}\), \(m_{bd}\), \(m_{ce}\), and \(m_{ce}\) are sent every 80 slots. Figure 6 shows the end-to-end delay of messages \(m_{ga}\), \(m_{ag}\), \(m_{db}\), \(m_{bd}\), \(m_{ce}\), and \(m_{ce}\). It summarizes the results of ten simulations with various initial random-values. It is important to note that packet delivery rate of all simulations is 1.0, meaning that all messages have been delivered. Moreover, all of them satisfy their deadlines, as network goodput ratio is 1.0. In this case, we defined the deadline as in Equation (15). We can also observe that there is a high dispersion of end-to-end delay values, particularly large for messages with the highest number of hops. Moreover, it does not seem to follow any trend, as it presents continuous changes over time. In this way, Figure 7 shows the oscillating behavior of the message delays for the first 2500 slots. This can be explained by the huge number of messages that are pending to be sent by a node (own messages or in-transit messages), which is known as the Bufferbloat effect [66]. Figure 8 shows the queue occupancy (number of messages) of nodes \(a\) to \(e\) for the first 400 slots. Notice that a node can only transmit a single message per frame (11 slots). Therefore, these pending messages in queues cause the self-adaptation of messages to go through other paths, involving nodes with fewer pending messages. Table 8 shows the path usage of a message going from the same initial node to the same final node. Finally, we also observed that the delay of opposite paths do not necessarily need to be the same, as we can see in Figure 6 considering the delays of messages  
Figure 5: Example of end-to-end delays over time. (**a**) Messages from node \(g\) to node \(a\); (**b**) Messages from node \(d\) to node \(b\). Figure 6: End-to-end message delays. model deals with a uniform distribution that has constant probability. Unfortunately, this failure model is memoryless, which means that it does not reflect the bursty nature of failures, also known as the long-range dependency. For a more realistic model, a self-similar process such as the Pareto distribution can be used as a long-tail failure-model. We have simulated two different approaches in terms of message dropping: (1) a fail every ten messages; and (2) a fail every two messages. This parameter is denoted as Mean Time Between Failures (MTBF). Notice that a two-message MTBF can be considered as an extreme failure-rate. Table 9 shows that packet delivery ratio (PDR) is 1.0 or nearly 1.0 when there is a fail every 10 messages, but it decreases significantly (close to 0.92) when there is a fail every 2 messages (extreme failure-rate). Anyway, all delivered messages are within the assumed deadline. We can also observe that these failures produce a slightly increase in the end-to-end delay when it is assumed a fail every 10 messages, and a higher increase (although not important) when it is assumed a fail every 2 messages. This difference is due to the fact that, in the presence of higher failure-rates, messages deal with more paths and more unusual ones. For instance, Table 10 shows the path usage of all messages analyzed for the Pareto distribution model, with fails every 10 messages and every 2 messages. There we can observe that the most popular path has similar percentage of use in both cases, but Pareto model (that fails every 2 messages) introduces more paths with small percentage of use, compared to the other failure approach. As explained in Section 6, we assumed an opportunistic routing-algorithm based on the epidemic model, as UW-ASN have a small traffic-intensity.