Wireless sensor networks are currently revolutionizing the way we live, work, and interact with the surrounding environment. Due to their ease of deployment, cost effectiveness and versatile functionality, sensors are employed in a wide range of areas such as environmental monitoring, surveillance or smart homes. While providing unprecedented opportunities for a variety of applications, current sensor networks face several challenges. For instance, the reliability of sensor measurements is often affected by the position of the sensors relative to the monitored object/phenomenon or the characteristics of the surrounding environment. It is, thus, often needed that several sensor measurements are retrieved so that reliable information about a monitored area is acquired. Moreover, since sensors can only function with sufficient energy, their functionality is affected by their limited energy resources. In this thesis, we employ the theory of stochastic processes and queueing, combinatorial theory, as well as optimization techniques such as stochastic dynamic programing to analyze the performance of wireless sensor networks, with a focus on data retrieval time, energy consumption and measurement reliability constraints. The focus of this thesis is three-fold. Firstly, we analyze the time needed to retrieve a fixed number of sensor measurements from a wireless sensor network. Based on these measurements, an aggregate is obtained. We take into account aspects such as transmission interference, limited, stochastic energy availability induced by the fact that the sensors harvest energy from the environment, limited transmission bandwidth. Given these assumptions, we analyze the retrieval time of measurements under centralized and decentralized sensor transmission schedules. While the centralized schedules are optimal with respect to the retrieval time of measurements, the decentralized schedules require less coordination between the sensors and are more suitable for implementation in practice. Nonetheless, the degree of difference between the two types of schedules, which we derive in this thesis, indicates the degree of improvement that distributed schedules can achieve. Secondly, we consider wireless caches, randomly deployed in the plane, that store a data file in a distributed manner. We provide an exact characterization of the Pareto front of two conflicting objectives concerning the cost of deploying the caches in the plane and the energy cost of retrieving the data file from these caches. We analyze the Pareto front under a partitioning and a network coding data caching strategy. Pareto dominance is proven for the network coding strategy, which shows that allowing for additional complexity for caching strategies, as is the case of network coding, leads to savings in terms of both energy and deployment costs. Thirdly, we consider the case where sensed data is retrieved by querying either the wireless sensor network or a central database. We formulate an optimal query processing strategy with respect to the response time of queries and the quality (freshness) of the query data. To determine this optimal strategy, we employ a discrete-time Markov decision process, which is derived by non-standard, exponential uniformization of a continuous-time Markov decision process with a drift. We compare numerically the performance of this optimal policy with several, simple query processing heuristics, and show under which system parameters these heuristics perform close to the optimal with respect to the query response time and data quality (freshness). Overall, the mathematical models and results derived in this thesis aim to provide a formal, theoretical support for the design of wireless sensor network applications related to the retrieval of reliable data, query-based sensing and data caching, with a goal of assisting the implementation of such applications.
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