## 4 Control Packet Collision  
In this section, we discuss the control packet collision problem in IRDT together with some novel approaches to resolving it. One problem related to IRDT is collisions between ID packets and other packets, as well as collisions between SREQ packets, which we refer to as 'ID collisions' and 'SREQ collisions', respectively. All nodes send ID packets periodically, and therefore ID packets can collide with other packets. Regarding SREQ collisions, the sender node returns an SREQ packet when an ID packet from a forward node arrives, as described in Section 3.2. Thus, if more than one sender receives an ID from a forward node, the sender nodes return SREQ packets simultaneously, the packets collide with each other. In this case, the sender nodes remain awake in wait for another ID, and as a result their energy consumption increases. Furthermore, SREQ collisions are in danger of recurring at nodes that are the  
Figure 4: Classification of neighboring nodes at node 3.  
Figure 5: An example of a routing function.  
only forward nodes for their backward nodes. For example, this'recurring SREQ collision' often occurs at the sink node, which is the only forward node for its neighbor nodes. After an SREQ collision occurs at the sink node, more than one neighbor node still contains data packets. This causes another SREQ collision following the ID transmission by the sink node. Due to the scheduled timer for discarding data (set to \(T_{d}\)) built into all nodes, recurring SREQ collisions eventually cease. Since the sender continues waiting for an ID packet until the sender receives a DACK packet from a receiver, recurring SREQ collisions lead to large energy consumption, as shown in Figure 6. For the above reasons, a reduction of the respective rates of ID and SREQ collisions (collectively denoted as \"control packet collisions\") is meaningful in terms of energy efficiency.  
Next, we describe the influence of the intermittent interval on the probability of packet collisions, as well as the procedure for determining a proper intermittent interval which decreases this probability. Changing the intermittent interval affects the following two aspects:  
1. Probability of SREQ collisions This is the probability with which multiple nodes return SREQ packets simultaneously immediately after a receiver node sends an ID packet. Since SREQ collisions are caused by data packet congestion, a longer intermittent interval increases this probability. If SREQ collisions occur, the energy consumption of the sender nodes increases due to retransmissions. Furthermore, such SREQ collisions can occur repeatedly.
2. Probability of ID collisions This probability corresponds to the likelihood that ID packets sent periodically by all neighboring nodes collide with SREQ or data packets. It is clear that a shorter intermittent interval increases this probability. As in the case of SREQ collisions, retransmissions increase energy consumption.  
We propose three methods for resolving the control packet collision problem, namely, reactive and proactive control of the intermittent interval and data aggregation. A protocol using the reactive method starts avoiding SREQ collisions soon after the first SREQ collision occurs. The advantage of this method is adaptability to changes in the network topology and the packet generation rate. In comparison,  
Figure 6: Recurring SREQ collisions; A major cause of excessive energy consumption in sender nodes.  
in the proactive method, the optimal intermittent interval which minimizes the sum of the respective probabilities for SREQ collisions and ID collisions is obtained analytically, where each node knows its own traffic load. We refer to this intermittent interval as the \"proper interval\" (denoted as \(T^{*}\)). Finally, data aggregation can be used to decrease the number of data packet transmissions for each node, which can decrease the probability of SREQ collisions.