## 4 Performance Evaluation
### Hidden-Terminal Topology
Obviously, keeping the sink and devices awake all the time or for long time intervals (high duty cycle) will shorten the latency at the expense of energy consumption. This contradicts one of the basic goals of typical WSNs. Note that the packet formation instance is application-dependent. Hence, the time between packet formation and sink wake-up, which determines a lower bound on the sojourn time, cannot necessarily be coordinated. However, in both protocols, the device can synchronize additional awakening time with its intended receiver (the sink) such that a device will have its awakening time instance as a receiver, and in case it is backlogged, it will schedule an additional wake-up instance according to its intended receiver's wake-up time (e.g., Wise-MAC [45] and PW-MAC [43]), which, in turn, will reduce the duty-cycle. The results presented above are averaged over all devices that are dispersed over the inspected region; hence, they combine devices that are in sensing range of one another and others that are hidden from one another. One might suspect that the performance degradation of devices that have more hidden terminals is offset by the performance of devices with no or few hidden terminals. Accordingly, we examine the performance of one of the devices that is located in one of the corners. Note that the chosen device contends with devices that are hidden from it (dispersed around the other three corners of the region) and with devices that are within its sensing range. Surprisingly, as can be seen in Figure 16, even though performance is expected to be more exposed to hidden devices and, hence, to suffer from more collisions than other devices, the results attained by the selected device (Device-3) in all three performance metrics (sojourn time, duty cycle, and latency because both the transmitting device and the sink are awake) are quite similar to the average ones. However, recall that, since the packet transmission time is quite short compared to the cycle itself, the penalty for collision is negligible. Moreover, each collision delays all queueing packets and keeps all backlogged devices awake regardless of whether they were the ones involved in the collision. All the more so, since the window grows for all the devices collectively, collisions by any devices, regardless of their location or topology, affect all the devices' contention windows similarly; hence, their performance is equally affected. Figure 16: Hidden-terminal topology: The performance of a specific device (Device 3) for a topology comprising 50 devices under various mean inter-arrival times (\(\lambda\)). (**a**) Sojourn time. (**b**) Duty cycle. (**c**) Latency because both the transmitting device and the sink are awake. Next, we examine the effect of \(K\) on the performance of MAR-RiMAC. Recall that \(K\) defines the number of reservations that can be transmitted simultaneously. We examined different \(K\)s (\(K=2,4,8,16\)) in the 50 devices with a hidden-device topology under different loads. Figure 17 shows the sojourn time, duty cycle, and latency. Surprisingly, Figure 17 clearly depicts that \(K\) has a marginal effect on all three performance criteria. Since a greater \(K\) results in a higher number of reservations that can be transmitted and be decoded simultaneously, one could have expected that MAR-RiMAC performance would improve when increasing \(K\), all the more so since, in our simulations, we kept a fixed \(T\), i.e., the overhead while increasing \(K\) was kept constant. However, in MAR-RiMAC, even for small \(K\), when more than \(K\) devices try to reserve a transmission simultaneously and a collision between these reservations will occur, not only is the collision very short (RtT) signals are very short), but the collision resolution procedure is also very short, and the loss due to this collision resolution mechanism is negligible compared to the cycle duration.