Equilibrium Transmission Bi-level Energy Efficient Node Selection Approach for Internet of Things

Abstract

The Internet of things concept is based on data from sensor devices. The conservation of sensor data in the cloud has become a well-known challenge with respect to the sensor-cloud network. There is an enormous quantity of sensed data, including missed and unimportant data due to unavailability of the node, low link quality, node deficiency or latency in path communication. In order to address this issue, it is necessary to develop an accurate sensor selection approach, precisely for the purpose of reducing the quantity of unimportant data (missed and noisy data). In this paper, we formulate an innovative and efficient bi-level node energy assessment algorithm, named BNSA, which uses a belief propagation protocol for optimal energy-efficient sensor selection. On the first level, the equilibrium transmission energy function is applied to all nodes to evaluate the transmission rate and link quality, together with the residual energy of the node, to predict the energy consumption, providing an accurate prediction of the energy level of the nodes. On the second level, optimal nodes are selected based on the prediction of the energy level. Belief propagation draws inferences for revealing missed sensor data. This approach improves the lifespan of the network and reduces the energy utilization rate by more than 32.3% with a delay rate of 77%. This is reflected in an enhancement of the quality of service with 85% of the energy consumption over the network, compared with existing models.

Appendix

Theorem T.1

Deploying additional nodes if $d(a,b) \ge R\,\,and\,\left| A \right| \le \left| \varDelta \right| (\frac{m}{\delta } + 1)$

Proof

The distance between all nodes are evaluated as

$$\begin{aligned} \sum \limits _{a,b \in S}^n d(a,b)= & {} \sqrt{\sum \limits _{i = 1}^3 {x_i^{{a_1}} -x_i^{{b_1}}}} + \sqrt{\sum \limits _{i = 1}^3 {x_i^{{a_2}} - x_i^{{b_2}}}} \\&+ \sqrt{\sum \limits _{i = 1}^3 {x_i^{{a_3}} - x_i^{{b_3}}}} + \cdots + \sqrt{\sum \limits _{i = 1}^3 {x_i^{{a_n}} - x_i^{{b_n}}}}\\= & {} \sqrt{\varDelta _{a,b}^1} + \sqrt{\varDelta _{a,b}^2} + \sqrt{\varDelta _{a,b}^3} + \cdots + \sqrt{\varDelta _{a,b}^n}\\= & {} \varDelta _{a,b}^n \le {R_{The}} \end{aligned}$$

Let ${\varTheta _l}$ be the set of data points of $\{{\rho _i}\}_{i=1}^m$, which are still not inserted after step l, with ${\varTheta _0}= \{ {\rho _i}\} _{i = 0}^m.$

The highest number of uncovered data points over ${\varTheta _l}$ in step $l + 1$. Hence, the size of this sub-area must cover at least $^{\varTheta _l}\big / \delta$ information/data point in ${\varTheta _l}$, where $\left| {{\varTheta _l}} \right|$ denotes the amount of data points in ${\varTheta _l}$. If this spacious sub-area covers fewer points, it is difficult to cover ${\varTheta _l}$ with $\delta$ data points, which repudiates the presence of $\delta$.

Such that, we have $\left| {{\varTheta _{l + 1}}} \right| \le \left| {{\varTheta _l}} \right| - ^{|\varTheta _l|} \big / \delta$ and since

$$\begin{aligned}&\left| {{\varTheta _l}} \right| \le \left| {{\varTheta _{l - 1}}} \right| - {{\left| {{\varTheta _{l - 1}}} \right| }\big / \delta } =\left| {{\varTheta _{l - 1}}} \right| \left( 1 - \frac{1}{\delta }\right) \nonumber \\&\quad \le \left| {{\varTheta _{l - 2}}} \right| {\left( 1 - \frac{1}{\delta }\right) ^2}\nonumber \\&\quad \cdots \nonumber \\&\quad \left| {{\varTheta _0}} \right| {\left( 1 - \frac{1}{\delta }\right) ^l}\nonumber \\&\quad = m{\left( 1 - \frac{1}{\delta }\right) ^l} \end{aligned}$$

(T.1)

When $\left| {{\varTheta _l}} \right| < \delta = \left| \varDelta \right|$, we resolve for l as follows

$$\begin{aligned} m{\left( {1 - \frac{1}{\varDelta }} \right) ^l} = \delta \end{aligned}$$

(T.2)

Since, ${(1 - x)^{\frac{1}{x}}} \le \frac{1}{\delta } \forall \,{\textit{for}}\,{\textit{all}}\,\,x,\,{\textit{we}}\,\,{\textit{have}}$

$$\begin{aligned} l \le \delta \left( {\frac{m}{\delta }} \right) \end{aligned}$$

(T.3)

Thereafter, remaining only $\delta$ information points need to process. Because each succeeding level excludes at least one data point, so $\left| A \right| \le \left| \varDelta \right| \left( {\frac{m}{\delta } + 1} \right)$, make an accurate decision making results with QoS of service, better communication without loss of data even at abnormal conditions. $\square$