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.