
Table 1: Power devices and parameters for the energy model.

![0_image_0.png](0_image_0.png)

Data Device specifications

Tx/Rx (4 bytes) 7.43µC

Radio On 12.8mA

Radio Off 0.025mA

Battery capacity 2600µC

Energy harvesting (f) 1.6W

Max. Tx Power 500m

intensity into energy:

$$e_{i}^{\rm hav}((t-\Delta,t]):=f\cdot\int_{t-\Delta}^{t}s(z)\cdot(1-c(z))dz\tag{4}$$

![0_image_1.png](0_image_1.png)

In the experiments presented in this article we do not consider any specific user application, that is, the energy consumption of phase two of the proposed protocol must be simulated. This is done by removing an amount of eapp of energy from the battery for each execution of phase two. The parameter values used for simulation are as follows:

 | $p_{\rm min}$ | $p_{\rm max}$ | $g$ | $p_{\rm a}$ | |:----------:|:----------:|:----------:|:----------:| |  0.07   |  0.14   |  0.1   |  0.00   | |  

pmin pmax g pa eapp f
0.07 0.14 0.1 0.001 0.001 0.0027
It is important to note that the information which refers to the power profile of the iSense nodes is obtained by properly rescaling the values from Table 1 to the [0, 1] range that is used by the description of duty-cycling given in Section 3.

## 4.1 Experiments

Assuming that ∆—that is, the length of one period—corresponds to 60 seconds, the simulations that we conducted span 30 days (each day consists of 1440 periods). The first phase of each period, which is reserved for the duty-cycling events, was given 0.05 seconds. Information about the state of the sensor nodes (active versus inactive) is collected at the start of each period. The most important measure taken is the *mean activity* of the sensor network, which is measured—at any time—as follows:

$$A:={\frac{1}{k}}\sum_{i=1}^{k}a_{i}\in[0,1]$$
$$({\boldsymbol{5}})$$

ai ∈ [0, 1] (5)
Note that, the greater A the more sensors are active at the specific time at which A was determined.

Self-synchronization behavior is characterized by an oscillating value of A over time. This was shown already for a mobile sensor network with k = 120 sensor nodes in Figure 1 of the introduction (see solid line). However, the results from that figure were obtained in a *perfect environment* with no collisions or transmission failures and no propagation times. Moreover, the energy model that was used had no relation to real sensor node hardware.

The experiments that we present in this section aim at proving the applicability of the proposed mechanism in real sensor networks. All experiments are done on the basis of a static network of k = 120 iSense nodes as simulated by the Shawn sensor network simulator. For the first experiment that we conducted we assumed a zero probability for packet collisions. Moreover, we assume a cloud density of zero, that is, c(z) = 0 for z ≥ 0. Figure 3 shows the obtained duty-cycling behavior.

Again, the solid line shows the fraction of active sensor nodes over time, whereas the slashed line shows the average battery level of the sensor nodes over time. Finally, the dotted line represents the sun power that is used to establish the amount of energy which can be harvested by the sensor nodes at