Mihaela Mitici

Optimal deployment of caches in the plane

We consider wireless caches placed in the plane according to a homogeneous Poisson process. A data file is stored at the caches, which have limited storage capabilities. Clients can contact the caches to retrieve the data. The caches store the data according to one of the two data allocation strategies: partitioning & coding. We consider the Pareto front of the expected deployment cost of the caches and the expected cost of a client retrieving the data from the caches. We show that there is a strong trade-off between the expected retrieval and the expected deployment cost under the partitioning and the coding strategies. We also show that under coding, it is optimal to deploy a high number of caches, each with low storage capacity.

Energy-efficient data collection in wireless sensor networks with time constraints

We consider the problem of retrieving a reliable estimate of an attribute from a wireless sensor network within a fixed time window and with minimum energy consumption for the sensors. The sensors are located in the plane according to some random spatial process. They perform energy harvesting and follow an asleep/awake cycle. A sink, at a random location in the plane, requests measurements from the awake sensors in order to retrieve an estimate of an attribute. The sink has to collect a sufficient number of measurements within a fixed time window. Moreover, the sink aims to minimize the energy that the sensors use to transmit their measurements. We determine a closed-form expression for the expected energy consumption of the sensors when measurements are retrieved according to a Greedy schedule. We also provide an upper bound on the maximum expected distance over which a sensor transmits under this Greedy schedule. Furthermore, we formulate a Markov Decision Process (MDP) to determine a sensor transmission schedule with general time constraints. We also develop a heuristic that schedules the sensors for transmission. We compare numerically the performance of the MDP schedule with the heuristic and with an offline, optimal schedule, where the asleep/awake state of the sensors is assumed to be known ahead of time. We show that the energy consumption under the MDP schedule converges to the energy of the offline schedule as the size of the time window for measurement collection increases. We also show that the heuristic performs close to the MDP schedule in terms of energy consumption.

Deployment versus data retrieval costs for caches in the plane

We consider the problem of finding the Pareto front of the expected deployment cost of wireless caches in the plane and the expected retrieval cost of a client requesting data from the caches. The data is stored at the caches according to partitioning and coding strategies. We show that under coding, it is optimal to deploy many caches with low storage capacity. For partitioning, we derive a simple relation between the cost of the cache deployment and the cost of retrieving the data from the caches. We quantify the improvements offered by optimal coding in comparison to partitioning, i.e., we derive a relation for the difference in deployment cost required to achieve a given retrieval cost. Finally, we show that even non-optimal coding is better than partitioning in the sense that no coded deployment can be dominated by a partitioning strategy.

Performance analysis of data retrieval in wireless sensor networks

In this thesis, we employ the theory of stochastic processes and queueing, combinatorial theory, stochastic dynamic programing to analyze the performance of wireless sensor networks, with a focus on data retrieval time, energy consumption and measurement reliability constraints. 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. We analyze the retrieval time of measurements under centralized and decentralized sensor transmission schedules. 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. Thirdly, we consider the case where sensed data is retrieved by querying either the 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. 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 heuristics, and show under which system parameters these heuristics perform close to the optimal with respect to the query response time and data quality. The 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, with a goal of assisting the implementation of such applications.

Decentralized vs. centralized scheduling in wireless sensor networks for data fusion

We consider the problem of data estimation in a sensor wireless network where sensors transmit their observations according to decentralized and centralized transmission schedules. A data collector is interested in achieving a data estimation using several sensor observations such that the variance of the estimation is below a targeted threshold. We analyze the waiting time for a collector to receive sufficient sensor observations. We show that, for sufficiently large sensor sets, the decentralized schedule results in a waiting time that is a constant factor approximation of the waiting time under the optimal centralized scheme.