# Integrated Evaluation of Reliability and Power Consumption of Wireless Sensor Networks
## 7 Related Work
### Power Consumption  
Different formal techniques have been used to model and evaluate the energy consumption of WSNs: Petri nets [25; 26], queuing Petri net (QPN) [27], Colored Petri net [16; 18], Markov chains [28; 29], Finite State Machines [30; 31], process algebras [32]. [PERSON] [25; 26] used Petri nets to model processors of WSN nodes. By using the proposed models, he estimates the average CPU power consumption. Besides, the model is also used to understand the energy consumption at the network layer of the cross-layer energy-aware routing. [PERSON] [27] presented an event-driven queuing Petri net (QPN) model to simulate the power consumption of WSN nodes. Each node has an energy source (battery) and a set of components, such as microcontroller, receiver and sensors. In turn, each component has its power states and some preset state transitions that define its power behaviour, which is modelled in QPN. While the power evaluation is based on QPN, reliability issues are not considered in this evaluation. [PERSON] [16; 18] proposed the use of Coloured Petri nets to evaluate the power consumption of both the sensor network lifetime and WSN application executing in the node. This approach consists of a fully automated process for assessing the WSN lifetime, a set of reusable Coloured Petri Net models to express the power consumption of WSN communication protocols, and a strategy for comprising CPN models of WSN applications and protocols. [PERSON] [28] presented a Markov chain-based cross-layer model to study the statistics of power consumption of WSNs. In particular, this work captures the probabilistic distribution of the energy consumption. In practice, instead of the average power consumption, this approach produces the probability that the consumed power in a given period is lower than a particular threshold. [PERSON] [29] designed two battery models (linear and non-linear) to perform a parametric evaluation of the longevity of WSN nodes. The linear model is based on a Markov reward model that allows capturing the battery consumption of the WSN node and determining some reliability parameters. Meanwhile, the non-linear model is based on continuous phase-type distributions and Kronecker algebra. [PERSON] [30] defined a power consumption model based on finite state machines. In particular, the model is used for an online account, simulation and generation of a prior knowledge of the WSN. The proposed model consists of FSMs that defines states and transitions of WSN nodes' hardware, in such way that moving through the model and summing up annotated energy values enable us to estimate the power consumption of the node. [PERSON] [31] designed FSMs (Finite State Machines) to model the behaviour and interactions of WSN node elements, namely processing, communication and control units. In particular, the emphasis is on the communication unit where every transition of the FSM alters the energy consumption of the node. The measurements of the actual consumption of ZigBee and Wi-Fi communications feed their respective FSMs. [PERSON] [32] proposed a framework for modelling WSNs that can be used to evaluate their power consumption. The framework is based on a probabilistic process algebra whose functioning is driven by Markovian probabilistic schedulers. The use of a process algebra allows checking temporal logic properties using model checkers. Each WSN node along with its location is represented in such way that probability distributions drive the node mobility. More recently, [PERSON] [33] adopted a Genetic Algorithm (GA) in a solution to monitor targets in WSNs. GA is used to optimise the monitoring coverage of non-stationary sensor nodes and to maximise the network lifetime. The proposed algorithm utilises information, such as the coverage range of individual sensor nodes, distance to base station and expected consumed energy, to choose the sensor cover that minimises the power consumption to monitor the targets.