## 1 Introduction  
Wireless Sensor Networks (WSNs) are special ad hoc networks composed of a large number of low-cost, low-power, and low-rate wireless devices (i.e., sensor nodes) with capability for sensing and, occasionally, actuating upon the environment where they are deployed. WSNs can be used to support multiple types of applications, such as: health, structural and environmental monitoring, home automation, vehicular systems, military applications, and many others [1; 2; 3]. In addition, due to their specific characteristics such as: flexibility, mobility, autonomous and collaborative operation, WSNs can be deployed in hazardous or hostile environments, where the human presence or the use of wired systems are unsuitable [4]. Recent advances in Micro-Electro-Mechanical systems (MEMs), microprocessors and low power radio technologies [2, 3] enable the availability of sensor devices increasingly robust, with more storage and processing capabilities, and at a lower price. In this context, the implementation of WSN wide-scale applications with energy-efficient and time-sensitive requirements have become an attractive research topic. The IEEE 802.15.4 standard [5] and the ZigBee specification [6] define a set of networking topologies commonly used in WSNs. The IEEE 802.15.4 defines PHYsical (PHY) and Medium Access Control (MAC) sublayers for Low-Rate Wireless Personal Area Network (LR-WPAN), focusing on short-range operation, low-data rate, energy-efficiency and low-cost implementations. The IEEE 802.15.4 standard basically defines two types of devices: a Full-Function Device (FFD) and a Reduced-Function Device (RFD). A FFD is capable of serving as PAN coordinator, cluster coordinator, or simple device, while a RFD is only capable of serving as simple device. Besides that, while FFD nodes can perform routing and management activities, RFD nodes are just able to communicate directly with their coordinator nodes. A Wireless Personal Area Network (WPAN) is composed of multiple FFD and RFD devices, with a unique FFD acting as PAN coordinator. IEEE 802.15.4 defines two types of topologies: star and peer-to-peer. In a star topology, all sensor nodes directly communicate with the PAN coordinator. Thus, the network range is limited by the transmission range of its nodes, which is an impairment for wide-scale deployments. On the other hand, peer-to-peer topologies allow the implementation of more complex network formations, such as mesh and cluster-tree. Mesh networking topologies use a decentralised communication paradigm, allowing multihop routing from any node to any neighbour node. Mesh topologies allow network flexibility and provide high routing redundancy and good scalability [7, 8]. However, due to the lack of synchronisation mechanisms of traditional mesh networks, this topology type commonly does not allow nodes to enter into low power mode to save energy [9, 10], which significantly reduces the network lifetime. Moreover, it introduces additional complexity to ensure end-to-end connectivity [7]. These characteristics are undesirable for typical WSN-based monitoring applications, where power consumption and lower complexity are crucial issues. The IEEE 802.15.4e-2012 standard [11] was released to enhance the real-time properties of IEEE 802.15.4 MAC protocol and to increase the network scalability by using the DSME (Deterministic and Synchronous Multi-channel Extension) protocol, that provides synchronisation mechanisms for mesh topologies. The DSME protocol was incorporated into the newest version of the IEEE 802.15.4-2015 standard. This extension is out of the scope of this work, which is focused on the single-channel version of the IEEE 802.15.4 protocol used by the majority of WSN deployments. The cluster-tree hierarchical topology enables setting-up wide-scale deployments through a mesh of multiple neighbouring clusters. Therefore, cluster-tree topologies are preferable for setting-up wide-scale monitoring applications.