## 4 Performance Evaluation
### Clique Topology
\begin{table}
\begin{tabular}{c c c c} \hline \hline Bandwidth & 250 Kbps & Size of Hardware Preamble & 6 B \\ \hline Preamble & 192 μs & Size of ACK & 5 B \\ \hline Slot time & 320 μs & CCA Check Delay & 128 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation radio parameters. average inter-arrival time of 10 s/packet is 0.44 s for both the MAR-RiMAC and the RI-MAC protocols, while for an arrival rate of 1.1 packets/s (0.9 s average inter-arrival time), it is only 0.74 and 0.69 s for the MAR-RiMAC and the RI-MAC protocols, respectively. This result seems counterintuitive, as one could expect that high traffic loads result in higher collision probability with increasing numbers of retransmission attempts and, hence, higher delays. However, the fact that a device is staying awake longer allows it to receive an additional one or more packets for transmission while it is still awake, and to transmit them in the current cycle rather than delay its transmission until the next time that it is awake. Next, we examine the average duty cycle, which presents the percentage of time that a device is awake, and hence provides an indication of the device's power efficiency. Recall that the sleep cycle was set to 1 s; hence, a duty cycle of 5% indicates that, on average, the transceiver is active only for 50 ms/cycle. Figure 8 depicts the duty cycle results for the same set of topologies and parameters (e.g., mean arrival times) as those presented for the mean sojourn times. When examining the duty cycle, recall that, in addition to the periodic wake-up times in which devices need to transmit their beacons (RtR beacons) to announce that they are awake and to initiate potential transmissions to themselves, they need to stay awake in order to transmit backlogged traffic to the sink. Accordingly, the larger the load, the higher the duty cycle for both protocols. Specifically, the inter-arrival time affects the duty cycle in two ways: First, the lower the mean inter-arrival time, the more packets the device needs to send and the longer the time it needs to transmit these packets. For instance, even when there is no or very little contention, each time a device needs to send a packet, it needs to stay awake waiting for the sink to wake up before sending the packet. Second, when the mean inter-arrival time is low, more devices are backlogged and, in addition, to the time waiting for the sink to wake up, they need to stay awake longer waiting for their opportunity to transmit (contention resolution time). However, as before, the longer the sink is awake, the more probable it is that a device will find it awake and will not need to wait for its next  
Figure 7: Clique topology: Mean sojourn time for different numbers of devices and maximal number of simultaneous transmissions supported by MAR-RiMAC; \(K=4\). (**a**) Two devices. (**b**) Five devices. (**c**) Twelve devices. (**d**) Twenty devices. awake epoch. In addition, the longer a device stays awake transmitting packets back to back rather than distributing their transmission over multiple cycles, the shorter its awake time on average (e.g., a device transmitting 10 packets in one cycle while transmitting only its RtR beacon in the following nine cycles is less awake than a device transmitting the 10 packets at one per cycle). In Figure 8, it is evident that for a small packet size (28 bytes), the duty cycles of both protocols are quite similar. For example, in the 20-device topology, when the average inter-arrival time is 0.9 s/packet, the duty cycle is quite high: 24% for both the MAR-RiMAC and RI-MAC. When the load is low, even for the 20-device setup, the duty cycle is quite low (for an average inter-arrival times 10 s/packet, the duty cycles are 0.04% for both protocols), as devices are typically not backlogged, and can hence go to sleep immediately after waking up and transmitting their RtRs.