# Evaluation of Green Strategies for Prolonging the Lifespan of Linear Wireless Sensor Networks
## 3 Classification of Energy Management Techniques for Prolonging WSN's Lifetime
### Energy Consumption Analysis of WSN
#### 3.1.1 Analysis of the Energy Consumption of a Sensor Node
Assuming that at every cycle (time step \(k\)), which lasts for a total duration of \(T\), the sensor node undergoes a wake-up from sleep for a duration of \(T_{WUL,\ k}\) performs measurements for a duration of \(T_{SU,\ k}\), performs data processing for a duration of \(T_{proc,\ k}\), takes \(T_{WULT,\ k}\) to wake the transceiver up from sleep, perform data transmission and data reception for \(T_{TX,\ k}\) and \(T_{RX,\ k}\), respectively, and sleeps for a duration of \(T_{Sleep,\ k}\)[50; 51], then  
\[T=T_{WUL,k}+T_{SU,\ k}+T_{proc,\ k}+T_{WUT,\ k}+T_{TX,\ k}+T_{RX,\ k}+T_{Sleep,\ k} \tag{2}\]  
The energy consumed in the sleep state is given by  
\[E_{Sleep,k}=P_{Sleep,k}\times T_{Sleep,\ k} \tag{3}\]  
where \(P_{Sleep,k}\) and \(T_{Sleep,\ k}\) are the power consumption and the time duration in the sleep mode, respectively, at time step \(k\). The energy consumed in the active state is the sum of the energy consumed by the constituent parts of the sensor node and is given by  
\[E_{Active,k}=E_{PU,k}+E_{CU,\ k}+E_{SU,\ k} \tag{4}\]  
Figure 4: Components of a sensor node. where \(E_{PUL,k},~{}E_{CU,~{}k}\), and \(E_{SU,~{}k}\) are the energy consumed by the sensor node's processing unit, communication unit, and sensing unit, respectively, at time step \(k\). The processor's energy consumption, \(E_{PUL,k}\), is derived by adding the switching (dynamic) and leakage (static) energies in the circuits. Dynamic energy is the energy needed to activate parasitic capacitors on an IC from a digital zero voltage to a digital one voltage, while static energy is the energy dissipated as a result of the current leakage from power to ground that occurs constantly in the circuitry [52]. The energy consumed by the processing unit is given by  
\[E_{PUL,k}=P_{PUL,k}\times T_{PUL,~{}k}+E_{st,k} \tag{5}\]  
where \(P_{PUL,k}\) is the power consumed by the processing unit when it is active. This power is dependent on the operational frequency (\(f_{PUL,~{}k}\)) of the processing unit. \(E_{st,k}\) is the leakage (static) energy, and \(T_{PUL,~{}k}\) is the total duration for which the processing unit is active. \[T_{PUL,k}=T_{PUL,k}+T_{SU,~{}k}+T_{proc,~{}k}+T_{PUT,~{}k}+T_{TX,~{}k}+T_{RX,~{ }k} \tag{6}\]  
\[P_{PUL,k}=~{}\text{C}\times V^{2}\times f_{PU,~{}k} \tag{7}\]  
where C and \(V\) denote the switching capacitance and supply voltage, respectively, and \(f_{PU,~{}k}\) is the operational frequency of the processing unit. A major part of the processing unit's energy is consumed during data processing. The duration for data processing (\(T_{proc,~{}k}\)) is dependent on the operational frequency (\(f_{PU,~{}k}\)) of the processing unit and the number of instructions (\(N_{inst}\)). Thus, the energy consumption of the processor unit in the active state depends on the number of processed bits and the frequency of the processor based on the following equation:  
\[T_{proc,k}=\frac{N_{inst}}{f_{PUL,k}} \tag{8}\]  
Since the processing unit encompasses the memory unit in our model, the energy consumption of the processing unit is affected by the number of stored bits, the number of memory reads and writes, and the duration of storage. The energy consumed by the sensing unit is given by  
\[E_{total}=\sum_{k}\Big{(}E_{Active,k}+E_{Sleep,\ k}\Big{)} \tag{1}\]0  
where \(P_{SU,k}\) and \(T_{SU,k}\) represent the power of the sensing device and the duration of sensing, respectively. The energy consumption of the sensing unit is dependent on the sensor's coverage radius, the data generation rate, and the number of generated bits. The energy consumed by the communication unit is given by  
\[E_{total}=\sum_{k}\Big{(}E_{Active,k}+E_{Sleep,\ k}\Big{)} \tag{1}\]1  
where \(E_{TX,k}\) and \(E_{RX,k}\) are the power of the transceiver when operating in the transmit and receive modes, respectively.