Wireless Sensor Networks (WSN) have experienced an important revitalization, particularly with the arrival of Internet of Things applications. In a general sense, a WSN can be composed of different classes of nodes, having different characteristics or requirements (heterogeneity). Duty-cycling is a popular technique used in WSN, that allows nodes to sleep and wake up periodically in order to save energy. We believe that the modeling and performance evaluation of heterogeneous WSN with priorities operating in duty-cycling, being of capital importance for their correct design and successful deployment, have not been sufficiently explored. The present work presents a performance evaluation study of a WSN with these features. For a scenario with two classes of nodes composing the network, each with a different channel access priority, an approximate analytical model is developed with a pair of two-dimensional discrete-time Markov chains. Note that the same modeling approach can be used to analyze networks with a larger number of classes. Performance parameters such as average packet delay, throughput and average energy consumption are obtained. Analytical results are validated by simulation, showing accurate results. Furthermore, a new procedure to determine the energy consumption of nodes is proposed that significantly improves the accuracy of previous proposals. We provide quantitative evidence showing that the energy consumption accuracy improvement can be up to two orders of magnitude.

Wireless sensor networks (WSNs) and sensing devices are considered to be core components of the Internet of Things (IoT). The performance modeling of IoT–WSN is of key importance to better understand, deploy, and manage this technology. As sensor nodes are battery-constrained, a fundamental issue in WSN is energy consumption. Additional issues also arise in heterogeneous scenarios due to the coexistence of sensor nodes with different features. In these scenarios, the modeling process becomes more challenging as an efficient orchestration of the sensor nodes must be achieved to guarantee a successful operation in terms of medium access, synchronization, and energy conservation. We propose a novel methodology to determine the energy consumed by sensor nodes deploying a recently proposed synchronous duty-cycled MAC protocol named Priority Sink Access MAC (PSA-MAC). We model the operation of a WSN with two classes of sensor devices by a pair of two-dimensional Discrete-Time Markov Chains (2D-DTMC), determine their stationary probability distribution, and propose new expressions to compute the energy consumption based solely on the obtained stationary probability distribution. This new approach is more systematic and accurate than previously proposed ones. The new methodology to determine energy consumption takes into account different specific features of the PSA-MAC protocol as: (i) the synchronization among sensor nodes; (ii) the normal and awake operation cycles to ensure synchronization among sensor nodes and energy conservation; (iii) the two periods that compose a full operation cycle: the data and sleep periods; (iv) two transmission schemes, SPT (single packet transmission) and APT (aggregated packet transmission) (v) the support of multiple sensor node classes; and (vi) the support of different priority assignments per class of sensor nodes. The accuracy of the proposed methodology has been validated by an independent discrete-event-based simulation model, showing that very precise results are obtained.

Wireless Sensor Network (WSN) and the sensing devices are considered part of the core components of the Internet of Things (IoT). Hence, the modeling of IoT-WSNs is fundamental to having a better understanding, management, and deployment of this kind of technology. A fundamental issue in WSN is energy consumption due to the inherent limitations of this resource in the sensor devices. On the other hand, several issues arise in heterogeneous scenarios due to the coexistence of different sensor devices. Therefore, the modeling process becomes challenging and must consider the different transmission and operation cycles and modes that the transmission protocol implements to assure successful functioning in terms of transmission, synchronization, and energy savings. A duty-cycled MAC WSN protocol (PSA-MAC) has been modeled based on a pair of two-dimensional Discrete-Time Markov Chain (2D-DTMC), whose solution in terms of stationary probability distribution is used by expressions that have been derived to evaluate the energy consumption of sensor devices that could be used for WSN-based IoT applications. Analytical results of average energy consumption are obtained, where the synchronization, data, and sleep periods of a full transmission cycle are considered in a heterogeneous scenario with different node classes and priority assignments. Also, the normal and awake operation cycles are considered to assure synchronization and energy savings. Moreover, the transmission schemes of SPT (transmission of single packets) and APT (transmission of packets in aggregation) are also considered in the model. These results are validated through discrete event-based simulations, and the obtained results are accurate.

Teaching Algebraic Structures might represent some learning and understanding difficulties for the freshmen students of Industrial Processes Engineering at Universidad Autónoma de Sinaloa. In order to investigate the cause or causes of this situation, a diagnostic instrument (test) consisting of several questions was developed and was applied to a 40 engineering students’ group, about algebraic structures previous knowledge, mostly related with the conception of the real numbers laws. Although the subject of the real numbers laws is addressed for the first time in junior high and then delves in high school, the students reach the university without domain and sometimes without any knowledge of the subject. It will be part of this paper to present and discuss the results found in the diagnosis. It also highlights the importance and benefits of using a diagnostic instrument in subjects that are known to be difficult for students. Among the results that have been obtained, it is highlighted that there has been confusion about some properties of real numbers among students, and they make mistakes when trying to put them into practice. In particular, they often make mistakes when combining the implementation of a property within a subset of real numbers.