## 4 Control Packet Collision
### Collision Avoidance with Data Aggregation  
Data aggregation can reduce the number of data packet transmissions for each node. We assume that when a node aggregates \(m\) data packets, the size of the data packet increases \(m\) times, and the number \(m\) is appended to the ID packets in order to inform the receiver nodes about the identity of the sender node. Therefore, a larger \(m\) effectively decreases \(G(R)\) in Equation (6), and \(P_{SREQ}\) also decreases. Unfortunately, it increases \(T_{r}\) in Equation (5) as well as \(P_{ID}\). We present this trade-off in the following section. Here, we demonstrate the strong effect of data aggregation with sideward nodes. In [15], we presented a method in which each node gives priority to forward nodes as appropriate receivers. This is caused by data transmissions toward sideward nodes, which increases both the number of data relays and the consumption of energy. When using data aggregation, however, relay with sideward nodes is more effective since data aggregation with both sideward and forward nodes greatly decreases \(G(R)\). SREQ collisions can occur between two or more nodes even if they are not hidden. This occurs when the random numbers for two nodes selected through the binary exponential backoff mechanism coincide. For example, if node 3 and node 4 in Figure 6 are not hidden nodes, an SREQ collision might occur. However, if data aggregation at these nodes is performed well, only one node contains the aggregated data packet, and no SREQ collision occurs. Moreover, data aggregation can resolve recurring SREQ collisions which occur when there is only one forward node, such as a sink node. In our previous research, we demonstrated that these repeated SREQ collisions cause an increase in energy consumption. If IRDT does not use data aggregation, repeated SREQ collisions continue to occur until the sending time expires. Specifically, when data aggregation is possible, the priority of the forward nodes is extended  
Figure 9: Probability of control packet collisions. to sideward nodes which contain data packets. Whether sideward nodes receive data packets can be determined by adding this information to the ID packets. We limit the size of the aggregated data packets for the reasons noted above, namely, a large value of \(m\) increases both \(P_{ID}\) and the channel occupation time. We insert the number \(m\) into the ID packets in order to inform the receiver nodes about it, which can also be used to provide information about whether sideward nodes receive data packets. The use of this information prevents the data packet size from exceeding \(m\) times the original data size as a result of aggregation. Here, two methods can be used to add the functionality of data aggregation to IRDT:  
1. Maintaining intermittent operation for a fixed period of time: Sender nodes immediately begin to wait for an ID packet in IRDT when they receive or generate a data packet. At that time, data aggregation can be achieved by continuing their intermittent transmission of ID packets in order to receive data packets until the end of the fixed period of time without waiting for an ID packet, as shown in Figure 10(a). The node begins to wait for an ID packet when the size of the aggregated data packet reaches a certain predetermined size or a certain period of time passes. 2. Maintaining intermittent transmission of ID packets while waiting for an appropriate ID: In the current implementation of IRDT, the node which contains a data packet does not send an ID packet, although it is waiting for ID packets from other nodes. In order for sender nodes to receive  
Figure 10: Data aggregation procedures in IRDT. data packets while waiting for an ID packet, they alternate the processes of transmitting ID packets and waiting for an appropriate ID packet, as shown in Figure 10(b). When they receive an SREQ packet, they perform data aggregation, and when they receive an ID packet from an appropriate receiver, they cease the aggregation and transmit an SREQ packet.