## 4 Cross Layer Adaptation of Check Intervals
### Tree-Based Topologies
### Network Lifetime

The lifetime of the network is computed for each experiment according to Equation (2). We only consider values of DC above 10% which, based on our experiments, guarantee network connectivity. Note that for DC equal to 20%, network connectivity is guaranteed for tree topologies but not for linear topologies with \(p=5\) and \(p=10\). We compare the network lifetime using CLAC against the lifetime using CTP/BoX-MAC. We express the results of the network lifetime in days. Figure 9 illustrates the results for the 10- and 20-node linear topologies. We observe that the network lifetime decreases when DC increases, which matches the fact that a larger DC implies a bigger energy consumption. With a DC = 100% the lifetime converges to 5.5 days for all experiments. As the figure shows, a larger \(p\) implies a longer network lifetime. For positive values of \(p\), which implies a proportional increase of the delay, we obtain a lower DC and, subsequently, longer network lifetimes. This fact can be observed in Figure 9 where the longest network lifetimes are achieved for \(p=10\). From this figure we observe that CLAC improves the network lifetime when compared to BoX-MAC for all values of DC and \(p\). On the right hand side of Figure 9, we see network lifetimes more similar to CTP/BoX-MAC (except for DC = 20%). This behavior is due to the increase in the network size, which causes a bigger load for the forwarding nodes (remember that the network lifetime is the lifetime of the node that first dies). Figure 10 shows the network lifetime for 10- and 22-node tree-based topologies, both of which have a longer lifetime compared to linear topologies. In a linear topology, the node which is the nearest to the sink must receive N\(-\)1 packets and transmit N packets in each round, being N the number of nodes in the linear topology. It also accumulates the delays produced by each hop, which leads to high idle listening and consequently a lot of retransmissions. It follows that node 1 in a linear topology is very overloaded trying to receive and retransmit many packets, while, in the case of the tree, the overall traffic is split among the children of the root. Therefore, node 1 dies in a linear topology much earlier than in a tree topology. With a low DC the situation gets worse since the contention increases. For tree-based topologies the lifetime is increased, and CLAC doubles the lifetime obtained by CTP/BoX-MAC for some values of DC and \(p\). Figure 9: Network lifetime (in days) for 10-node (left) and 20-node (right) linear topologies. ### Packet Loss

We evaluate the packet loss in CLAC for DC greater or equal to 20% which, based on our experiments, guarantee network connectivity. As in the case of network lifetime, keep in mind that for DC equal to 20% network connectivity is guaranteed for tree topologies but not for linear topologies with \(p=5\) and \(p=10\). Specifically, we evaluate the packet loss ratio, which is defined as the ratio between the number of packets lost in CTP/Box-MAC over the number of packets lost in CLAC. Figures 11 and 12 illustrate the packet loss ratio for different values of \(p\); when this ratio is greater than 1.0 it indicates that there was more packet loss in CTP/Box-MAC than in CLAC. Figure 11 shows the packet loss ratio for the 10- and 20-node linear topologies. The packet loss ratio indicates that CLAC reduces the number of lost packets for most DC. Note that for \(p=5\) or \(p=10\), and DC = 20% the packet loss ratio is very high. This behavior coincides with the cases when the experiments do not yield a completely connected network. The lack of connectivity causes a high packet loss. According to the results, we can conclude that for DC greater or equal to 20%, which maintain the

Figure 11: Packet loss ratio for 10- and 20-node linear topologies. Figure 10: Network lifetime (in days) for 10-node (left) and 22-node (right) tree topologies. network connectivity and provide energy savings, CLAC may reduce packet loss.