## 3 Multiple-Access Reservation Receiver Initiation MAC (MAR-RiMAC)
### \"Request to Transmit\" (RtT) Signaling
Exactly as before, whenever a device wants to transmit a report, it waits for the inviting RtR in order to signal the sink that it is backlogged (has a report to send). Each RtR is followed by \(T\) conceptual minislots; each minislot duration is sufficient for the sink (report aggregators) to receive a signal from the furthest device, with sufficient time-guard boundaries such that there are no overflows to the sequential slot (starting at the current slot and leaking into the next slot). Immediately after receiving the RtR, a backlogged device, which is awake and waiting to transmit, transmits its transmission reservation indication (RtT) by following the pattern indicated by its exclusive sequence, such that the device transmits at each minislot that corresponds to it, which is 1 in its sequence, and it remains idle if it is 0. We denote minislots in which at least one of the active (signaling) devices is transmitting (the respective minislot index in its sequence is \"1\") as \"Active\", and minislots in which none of the signaling (waiting to report) devices are transmitting (the respective minislot index in all signaling devices' sequence is \"0\") as \"Idle\". After receiving the \(T\) minislots, the sink can identify the signaling devices merely based on the \"Active\" and \"Idle\" minislots. Note that consequently, it is sufficient for the sink to rely on a simple energy detection mechanism, which is sufficient to identify which minislots are \"Active\" and which are \"Idle\". After identifying the signaling devices, the sink pools their reports sequentially one at a time. The length of \(T\) and the construction of the code (the unique pattern assigned to each device) are determined based on the maximal number of devices that the sink can identify even when they signal simultaneously. Specifically, the mechanism is designed to support the maximal number of simultaneous transmissions. We denote this number by \(K\). In the event that the actual number of signaling devices exceeds \(K\), i.e., more than \(K\) devices are trying to signal simultaneously, the sink will not be able to identify the signaling devices, and a collision resolution mechanism should be invoked (the collision resolution procedure will be discussed in the sequel). This number of maximal supported simultaneous transmissions (\(K\)) should be configured based on the topology, the application  
Figure 5: Reuse of CSSs by multiple devices in the vacancy via a small contention interval. Device II and Device IV utilize the same CSS, yet choose different minislots; hence, they can be distinguished by the sink. Device I and Device IV choose the same minislot, yet utilize different CSSs; hence, they can also be distinguished by the sink. that the devices are performing, the performance constraints, and the device capabilities. The higher the \(K\), the greater the signaling overhead per se (i.e., the higher \(T\)), yet the smaller the collision probability (i.e., the greater the probability that more than \(K\) devices are trying to signal simultaneously). Accordingly, \(K\) should be chosen such that it balances between the signaling overhead and the collision probability, which requires invoking the collision resolution procedure, which also incurs waste of resources (overhead). The devices' sequences should be designed such that the sink will be able to identify the active devices provided that the number of active devices does not exceed \(K\). It has been shown that an efficient choice of parameters should be such that the ratio between the \"Active\" minislots (i.e., at least one of the active devices has 1 in its sequence and is, hence, transmitting) and the \"Idle\" minislots (i.e., all active devices have 0 in the respective minislot index in their sequence; hence, none are transmitting in this minislot) should be \(\frac{1}{2}\) irrespective of the actual active devices, i.e., for any set of \(K\) active devices (e.g., [55]).