Energy management for event capture in rechargeable sensor network with limited capacitor size

Abstract

Wireless rechargeable sensor nodes are usually equipped with capacitors which collect the the energy from RF signals and support the functioning of sensing, computation, and communication components. However, the highly limited capacitor size as well as the intrinsic energy cost during the node activation imposes critical design challenge for effective energy management. It is also desirable to realize effective coordination among nodes without too much intercommunication due to the highly limited energy capacity. In this paper, we consider the problem of how to schedule the activation of wireless rechargeable sensor nodes in order to maximize the event capture rate for random event process with the consideration of both highly limited capacitor size and activation energy cost. For the events following Poisson distribution, we theoretically prove that one optimal scheduling scheme for single node case is to activate the node only when the capacitor is fully charged and sleep only when the remaining energy is unable to support one activation. Then for the more general multi-node case, we propose a coordinated periodic scheduling scheme which reduces the activation overlap among different nodes without requiring the intercommunication. Extensive simulations are conducted to verify the effectiveness of our proposed methods.

Appendix

Proof

[Proof of Lemma 1] Assume θ is a schedule which does not obey the rule in the lemma. A sample path is displayed in Fig. 9, where b _i + r _i > B, but a _i = 0; after time i, θ keeps active for k slots and sleeps for l slots; and turns to active state again at time i + k + l + 1. We can see the energy overflow at time i. Thus b _{i + 1} = B.

Fig. 9

The original schedule θ

Based on this sample (note that $b_{i}^{\prime } = b_{i}$ and the recharge energy are the same), we design a new schedule θ′ (see Fig. 10): from time i, let the sensor keep active for m slots, where m = k if the sensor has enough energy, and m < k slots until the capacitor deplete; then keeps sleep for l + 1 slots; activate at time i + m + l + 1 again.

Fig. 10

The modified schedule θ′

It can be seen, since $a_{i}^{\prime } = 1$, the lost energy by $\theta$ is stored under schedule $\theta ^{\prime }$. From $b_{j} = b_{i+1} + \sum _{t=i+1}^{j-1} r_{t}-kc$ and $b_{j}^{\prime } = b_{i} + \sum _{t=i}^{j-1} r_{t}-[m+j-(i+m+l)]c,j = i+m+l+1,i+m+l+2,\ldots ,i+k+l$, since $b_{i+1} = B$ and $b_{i} + r_{i} > B$, it follows that $b_{j}^{\prime } - b_{j} = b_{i} + r_{i} - B + [k-m-j + (i+m+l)]c \ge [k-m-j + (i+m+l)]c$. Then the sensor can be activated at time j. Thus schedule $\theta ^{\prime }$ is executable. What’more, we can find under the new schedule, $b_{i+k+l+1}^{\prime }-b_{i+k+l+1} = b_{i} + r_{i} - B$. That is the sensor has more energy at time $i+k+l+1$ under schedule $\theta ^{\prime }$. If schedule $\theta ^{\prime }$ repeat n times, $n(b_{i} + r_{i}-B)$ units energy will be stored. When $n(b_{i} + r_{i} - B) > c$, we can let $a_{i+m+l}^{\prime } = 1$. Therefore schedule $\theta ^{\prime }$ is better than $\theta$. □