## 6 Automatic Active and Sleep (AAS) Model  
The node is periodically set into the sleep state in the duty cycling protocol [39]. The node can maintain a tradeoff between data latency and energy consumption by fixing the state of either sleep or wake-up automatically. The node consumes less energy at a higher latency for data delivery with a lower duty cycle. Once a node wakes up during its active duty cycle time, it should listen to the channel for a specific period of time to determine whether other nodes are available for communication. This situation creates difficulties and increases the overhead of the MAC protocol due to idle listening, which is a major source of energy consumption. The nodes continue to monitor the channel for incoming traffic, which increases energy consumption. Some of the WSN applications require transfer at a low data rate, but the sensor nodes remain idle for a longer period of time after performing their specific events. It is not advisable to keep the sensor nodes in the idle state for a significant period of time. Thus, the AAS model is integrated with BN-MAC to shorten the unnecessary idle listening time. Sensor nodes normally operate in two modes: ON and OFF. If the  
Figure 12: Message mechanism of the hybrid BN-MAC protocol. transceiver of the sensor node is active \"ON\" without performing any events, time delay and wasted energy result [40]. The unnecessary waste of energy can be reduced if the transceiver of the sensor nodes is controlled using the \"OFF\" state. We use the AAS model by setting the threshold value for the \"idle\" and \"OFF\" states to save energy. Let us assume that the energy consumed in the idle time of the sensor nodes should always be less than or equal to the \"OFF time\". Then \(E_{ittime}\leq E_{otine}\), where \(E_{ittime}\) is the consumption of the energy during the idle time and \(E_{ittime}\) is the energy consumed during the OFF time. Let us assume that \(\mathrm{E_{midle}(t)}\) is the minimum energy required for the sensor nodes to remain in the idle state, \(\mathrm{E_{idle}/_{on}}\) is the energy consumed by switching from the idle state to the \"ON\" state, and \(\mathrm{CS_{idle}/_{off}}\) is the energy consumed by switching from the idle state to the \"OFF\" state. Thus, the energy consumed in idle time can be computed using Equation (12):  
\[E_{ittime}*=\mathrm{E_{midle}(t)}\ +\ \mathrm{E_{idle}/_{on}}*\mathrm{CS_{idle}/_{ off}} \tag{12}\]  
Let us assume that \(\mathrm{CS_{on/off}}\) is the minimum amount of time required for the sensor nodes to consume energy by going from the \"ON\" state to the \"OFF\" state, \(\mathrm{CS_{off}/_{on}}\) is the time required for the sensor nodes to consume energy by going from the \"OFF\" state to the \"ON\" state, and \(E_{off}\) is the energy saved by the nodes when they are in the sleep state. Thus, the total \"OFF\" time energy can be calculated using Equation (13):  
\[E_{otine}=\mathrm{CS_{on/off}}+\ \mathrm{CS_{off}/_{on}}+\ E_{off} \tag{13}\]  
Let us assume that \(E_{otine}\), the total energy consumed during the \"OFF\" state, is larger than the energy consumed in the idle state, which was already proven and is given in Equation (14):  
\[E_{otine}\geq(\mathrm{CS_{on/off}}+\ \mathrm{CS_{off}/_{on}}+\ E_{off}\ ) \tag{14}\]  
Our goal is to transition the sensor nodes into the sleep state if no event is underway. Equations (12) and (13) indicate that the states of operations in the sensor nodes can be established automatically. Let us set the transition states \(\alpha\ (alpha)\) and \(\beta\ (beta)\) for sleep (OFF) and active (ON), respectively. An automatic change of transitions can be justified if Equation (15) is satisfied:  
\[CS_{\alpha}\ \geq max\ [0,(E_{attime}+E_{ittime}-\ E_{otine})*\ CS_{\beta\alpha}] \tag{15}\]  
where \(E_{attime}\) is the energy consumed during the active time and \(CS_{\beta\alpha}\) is the negligible amount of energy consumed by going from the active (OFF) state to the sleep (ON) state.