Average distance estimation in randomly deployed wireless sensor networks (WSNs): an analytical study

Abstract

A Wireless Sensor Network (WSN) is an energy-scarce network in which the energy is primarily dissipated by the sensor nodes during data transmission to the base station (BS). The location of the BS in a WSN dramatically affects the energy dissipation, the throughput, and the lifetime. While in a number of studies the optimal positioning of a BS is considered, the system parameters are optimized when the BS location is known in advance in many others. In this paper, we provide a general-purpose mathematical framework to find the expected distance value between every point within any n-sided simple polygon shaped sensing field and an arbitrarily located BS. Having the knowledge of this value is very imperative particularly in random deployment as it is used for energy-efficient clustering. Although similar derivations appear in the related literature, to the best of our knowledge, this study departs from them, since our derivations do not depend on the shape of the sensing field and the orientation of BS relative to it.In a deterministic deployment scenario, as there is prior knowledge about the locations of the deployed nodes, the average distance between each node and its neighbours, and similarly the average distance between deployed nodes and the BS, can easily be calculated. However, in the random deployment scenarios, the above mentioned distances, which indeed affect the energy consumption and thus the lifetime of an application, are not known before the deployment. Therefore, a probabilistic approach is required to estimate this average distance which would provide a beneficial tool for the network designers. For example, for a given number of sensor nodes that fulfil the required system parameters such as connected coverage, the network designer might need to estimate, if possible, the average distance between each sensor and a BS to adopt either multi-hop communication or single-hop communication before the deployment.In a number of RDWSN applications, each sensor node is assumed to reach the BS within a single-hop. However, in these applications which exploit direct communication, it is observed that a set of sensor nodes, which is distant from the BS, consumes a considerable amount of energy because it needs to perform long-haul direct transmissions. Therefore, these nodes, which are distant from the BS, tend to die early and thus shorten the lifetime of the network. To tackle this problem, multi-hop communication is usually taken into consideration because it is more energy-efficient than direct communication in such dense environments. In multi-hop WSNs, however, the nodes close to the BS have to forward data for the rest of the nodes that are away from the BS. Thus, they are again more likely to die earlier, causing the network to become partitioned and the network lifetime to get shortened. This is known as the energy-hole problem as is defined in Gong et al. (2013) and Du et al. (2015). Even before attempting to tackle an energyhole problem, the use of this estimated average distance to BS is imper...