## 4 Performance Evaluation
### Hidden-Terminal Topology  
In this part of the evaluation, we examine the protocols' performance under hidden-terminal topologies. In order to ensure that some of the devices are hidden from one another, we have limited the interference range of each device such that it will not cover the whole area. We positioned the sink at the center and set the transmission range to be slightly larger than the distance between the center and each of the four corners of the simulation zone, such that all devices, wherever positioned, can transmit directly to the sink. We further positioned four devices around the four corners of the simulation zone such that they were in transmission range with the sink but hidden from one another; the rest of the devices were randomly scattered over the simulation terrain. As before, we examined the performance under different numbers of devices and traffic loads. The results for the sojourn time and for the duty cycle for different numbers of devices and traffic loads are depicted in Figures 10 and 11, respectively. Figure 10: Hidden terminals: Mean sojourn time for different numbers of devices and \(K=4\). **(a)** Two devices. **(b)** Twelve devices. **(c)** Twenty devices. **(d)** Fifty devices. Figure 9: Clique topology: The sink’s mean duty cycle for different numbers of devices and \(K=4\). **(a)** Two devices. **(b)** Twenty devices. As can be seen in the figure, the sojourn time of RI-MAC is, as before, slightly shorter than that of MAR-RiMAC. However, this slightly shorter sojourn time is at the expense of a higher duty cycle, especially for high loads and for a moderate to high number of devices. The insight follows the same insight as with the clique topology, only the phenomenon is exaggerated. In particular, the collision probability, as well as the collision resolution time, for MAR-RiMAC is much lower than that of RI-MAC. Even for a low number of simultaneous-transmission devices supported by MAR-RiMAC (\(K=4\)), both the devices and the sink stay awake for much shorter time intervals to resolve collisions, and can go back to sleep much faster, i.e., the average duty cycles are lower. Consequently, since in RI-MAC, the sink stays awake for longer time intervals, more devices are waking up when the sink is awake; hence, they do not need to wait for the sink's wake-up time before starting to transmit their reports, thus shortening their expected delay. Furthermore, since in RI-MAC, devices are awake for longer time intervals to resolve collisions, they receive more packets while both they and the sink are awake, and can transmit them on the same cycle, back to back with their packets that arrived earlier, again shortening their expected delay. We explore the aforementioned long awake interval of the sink by exploring its duty cycle (recall that Figure 11 depicts the average duty cycle of all the devices). Figure 12a,b depicts a comparison between the sink's duty cycle for MAR-RiMAC and RI-MAC for the four- and 50-device topologies with hidden terminals. Figure 12c,d depicts the devices' average duty cycle, excluding the sink. It can indeed be seen that, with high loads, the sink's duty cycle in RI-MAC is much higher than the corresponding duty cycle in MAR-RiMAC. We further see that for the four-device topology, the sink's duty cycle in MAR-RiMAC is lower than the devices' average duty cycle (excluding the sink). However the sink's low duty cycle confirms the observation that a large part of the devices' awake time is spent waiting for the sink to wake up. Since in the presented results, the sink is never backlogged, it does not need to send data; hence, it does not need to wait for devices to wake up. After waking up and receiving all of the data (as there is no contention when \(K=4\)), it can go back to sleep. Note that even in the 50-device topology, despite the contention, the sink's duty cycle is lower than the devices' average duty cycle. In contrast,  
Figure 11: Hidden terminals: Mean duty-cycle for different numbers of devices and \(K=4\). **(a)** Two devices.