## 4 Cross Layer Adaptation of Check Intervals
### Tree-Based Topologies
However, the optimal value of \(p\) that provides the minimum packet loss is highly dependent on DC, the topology, and the network size. Figure 12 shows the packet loss ratio for 10- and 22-node tree topologies. CLAC significantly reduces the number of packets that are lost as compared to CTP/BoX-MAC, for all values of DC and \(p\), with the exception of DC = 50% in the 22-node tree topology. If we increase both the size of the network and the DC, the load of the network grows and the packet loss increases. We conclude that CLAC performs better in scenarios with DC less than 50%. ### End-to-end Delay

In order to show that CLAC does not increase the end-to-end delay, we measure the end-to-end delay for CLAC and BoX-MAC. First, we consider the 10-node linear topology where node 10 is the only data source and, second, we consider the 10-node tree topology with multiple sources: node 5, 7 and 9. In the 10-node linear topology, node 10 sends a data packet to node 0 (the sink) every 10 seconds. Within \(path(10,0)\) node 10 is 10 hops away from node 0. All the packets travel along the same path to achieve the destination, _i.e_., there is no changes in the topology. Figure 13 shows the end-to-end delay between node 10 and node 0 obtained for the linear topology with DC = 30%. The time that a packet takes from the source to the destination is the end-to-end delay, which we compute as the difference of the time of transmission and the reception. Each packet takes a variable amount of time to reach node 0, due to the effect of the retransmissions and the accumulated latencies. Figure 14 on the left presents the average end-to-end delay for a 10-node linear topology with only a source (node 10) for DC = 30%, 40% and 50%. We exclude the case of DC equal to 20% since it does not guarantee complete connectivity in the network. On the right hand side, we show the end-to-end delay for a 10-node tree topology for DC greater or equal to 20%, where nodes 5, 7 and 9 are data sources. Thus, we have: \(path(5,0)=\{5,4,2,0\}\), \(path(7,0)=\{7,6,4,2,0\}\) and \(path(9,0)=\{9,8,6,4,2,0\}\). We show the average end-to-end delay within \(path(9,0)\), which is the worst case. Figure 12: Packet loss ratio for 10- and 22-node tree topologies. In general when DC increases, the end-to-end delay is reduced, which matches the fact that a larger DC implies a lower contention. Even in the case where there is no contention due to the fact of having one single source (as represented by Figure 14 on the left), the end-to-end delay grows as a result of having strict duty cycles, _i.e._, we reduce the opportunity for fast forwarding and hence the penalty on the end-to-end delay. Note that when \(p\) increases the end-to-end delay also increases, since it is equivalent to reducing the DC. The end-to-end delay in the linear topology is larger than in the tree topology because of the difference in the path lengths, which is 10 hops for the linear topology and 5 hops in the tree topology. The average end-to-end delay of BoX-MAC is for most of the times between the end-to-end delay of CLAC with \(p=-1\) and \(p=1\). This result is within expectation since the DC used in BoX-MAC is above the DC used in CLAC with \(p=-1\) and below the DC used in CLAC with \(p=1\). It follows that the end-to-end delays depend on the duty cycles used and, correspondingly, present the same trend. Figure 14: End-to-end delay for 10-node linear and 10-node tree topologies. Figure 13: End-to-end delay between node 10 and 0 in a 10-node linear topology with DC = 30%. ## 6 Conclusions

The use of duty cycles to govern the radio activity of the nodes is extremely useful to limit their energy consumption. Preamble sampling-based protocols efficiently address this task by providing schemes to schedule the time at which the communicating nodes must turn their radio transceivers on and off. However, due to channel access contention and the internal processing (among other reasons), the times of radio activation in the sender and receiver may not match.