A Mathematical Modeling Approach for Optimal Trade-offs in a Wireless Sensor Network for a Granary Monitoring System

Over the years, wireless sensor networks (WSNs) have developed into a very promising field of research, providing diverse and novel applications and solutions to various challenges (Hodge et al., 2015) Most of the systems in the environmental applications of such networks have been observed to have inherent limitations and challenges, which include uneven coverage; cost ineffectiveness; cumbersome operability; high installation costs; being prone to damage, hazards, non-recyclability and limited coverage; high maintenance costs; high node failure rates; energy constraints; and offline data collection (non real-time) (Onibonoje et al., 2016). Various models and schemes have either been proposed or developed to overcome many of these challenges (Li et al., 2016); for example, mathematical models can be applied to the deployment, topology control and design of WSNs (Erdelj et al., 2016).

Power consumption optimization in sensor nodes is a major problem in WSN application design and implementation (Shirazi & Morris, 2017; Onibonoje, 2019). In many applications, limited resources are used to satisfy quality of service (QoS) requirements, and also useful to increase system lifetime with minimum energy consumption. Many of the deployments are made in environments where energy replenishment is very difficult, but not impossible (Arioua et al., 2016). Wankhade & Choudhari (2016) proposed an election-based scheme for energy efficiency in WSNs. In his study, the assessment of nominating cluster heads by the coordinator depends upon the associated surplus energy, residual energy and the location of individual nodes. Moreover, the shortest path to reach the coordinating node is selected by the cluster head by using the congested link. Lajara et al. (2015) proposed an approach to finding an analytic model to determine the charging state of the battery in wireless sensor nodes. The focus of their work was to derive modest models for accurately estimating the real state of batteries and accordingly evaluate the lifetime of the node.

A vital design issue in WSNs is energy consumption, with numerous data dissemination protocols and power management schemes specially designed for them. Protocols in WSNs are application-specific and depend on the application and network architecture; design emphasis has been placed on routing protocols which often differ. A classification of the different approaches of several possible routing protocols is presented (Zhao et al., 2017; Anasane and Satao, 2016).

Coverage control, as well as node localization, exist as basic problems in wireless sensor networks (Shamantha & Shirshu, 2016). Because of technical limitations, the detection capability of any sensor node is limited to a certain range. Use of a minimum number of sensor nodes to achieve coverage and connectivity requirements is an NP-hard problem. Wang (2011) formulated a mathematical model to calculate the number of nodes required to reach a specified coverage fraction, provided that some parameters are already determined. Hawbani et al. (2014) addressed coverage issues with the proposal of versions 1 and 2 of two grid-based algorithms, namely Grid Square Coverage. In addition, Hawbani & Wang (2013), provided a zigzag pattern-based algorithm for WSN coverage. The maximal and optimal coverage efficiency was reached by the algorithm when there was equality between the sensing range circumference for each node and the sum of its horizontal and vertical arc lengths.

There are also numerous WSN applications that necessitate mobility in sensor nodes. Conversely, security issues are increasing due to the mobility of sensor nodes in WSNs and their consequent susceptibility to numerous types of attacks (Ali et al., 2018). Key distribution and security in communication are the two emerging common issues in the authentication of mobile nodes in dynamic WSNs (Sarobin & Thomas, 2016). When sensor nodes move, there is always a requirement for repeated authentication from the central hub or other dedicated nodes (Deif & Gadallah, 2014). Pathak and Patil (2016) proposed an innovative protocol framework and a correlated mathematical model for key distribution and protected routing layer communication in mobile WSNs. On the basis of both static and dynamic situations, the model was applied to evaluate the performance of a diverse number of nodes, which eventually indicated that the framework was mainly suitable for dynamic WSN applications.

Mathematical models for specific wireless access in sensory networks were presented by Tymchenko et al. (2016). Their article reviewed and compared the special attributes of dedicated wireless sensor networks. The modules of the mathematical model for the prevailing dedicated wireless sensor network, which included signal propagation, communication graphs, and wireless channel models, were reviewed in the study. The study also explained the necessity for a topology control mechanism in WSNs.

The various current WSN models focus on addressing just one or two of the numerous challenges. However, achieving optimal trade-off between many objectives is presently a major challenge. Hence, the aim of this study is to present a mathematical model which represents a designed system that achieves optimal trade-off between the multi-objectives of environmental factors monitoring in WSNs. This is original work, with major applications in the modular storage systems of small-scale farmers and middle-level grain marketers. The novelty of the work contributes to the elimination of their inaccessibility to resourceful storage bins. The system can also be feasibly deployed for the effective monitoring of the existing large volume granary storage systems provided by governments in cities and major towns.