## 1 Introduction  
We are in era in which the Internet of things (IoT) has become a popular response to various technological challenges [1, 2, 3, 4]. RFID tags are commonly attached (or embedded) to things and wirelessly communicate to achieve certain goals. This creates complex wireless networks on which communication models are still a subject of research. Furthermore, WSNs have been deployed in various environments to assist moving objects such as drones and robots to perform various tasks [5, 6, 7]. Since its inception, the IoT, as a WSN, has provided critical assistance to humankind, especially in gathering information from hazardous environments. Indeed, the networks have the ability to collect, process, and transmit data from critical environmental conditions to safer places. These are some of the reasons they are now being used in various applications such as in agriculture, healthcare, environmental monitoring, military surveillance, structural monitoring, traffic control, and river level variation monitoring, etc. [8]. When data are collected in these networks, they are usually sent to a destination node called the Base Station (BS) for further processes [9]. These networks are usually made up of tiny sensor nodes. For the source of energy, the sensor nodes rely on rechargeable and replaceable batteries. However, charging and replacing these batteries is practically impossible when they are deployed in a hazardous environment. Therefore, the efficient use of the limited resources of the sensor nodes always helps to improve the performance of the network. The performance of a WSN can be improved by developing mechanisms (see [10; 11], for example) that can reduce the energy depletion of the nodes and extend the lifetime of the network. It is known that various units of sensor nodes, where the highest amounts of energy is being used are the sensing, data processing, and communication units. The communication unit is where the highest energy consumption is observed [12]. To minimize energy consumptions in these units many energy preservation techniques such as clustering, data aggregation, effective node deployment, cluster-based routing protocols, collection tree protocols, etc., have been developed. Hierarchical routing protocols, in WSNs, are seen as the most energy-efficient schemes and have been widely used [13]. Any of the schemes divide the network into groups called clusters, with each cluster having a head, a central node, called Cluster Head (CH). These heads receive the sensed data from the local nodes, aggregate the data and report to the Base Station (BS) through a single-hop or multi-hop communication approach depending on the distance from the BS. Some examples of such routing models can be found in [14; 15; 16]. In the related literature, there are several cluster-based routing algorithms that have been proposed in wireless sensor networks. In [17], a hierarchical routing has been proposed to successively improve the underling network lifetime. Here, the assumed network consists of two types of nodes (super nodes and monitoring nodes) which are all randomly arranged in an area of interest. However, the optimal network topology would improve the the performance of the proposed algorithm. To address this, the research work in [18] proposed a routing model where the considered network is \"properly\" chosen. This shows that the network deployment matters and is still a subject of research for the hierarchical routing models. More hierarchical routing model have been proposed in [19; 20] for optimizing the energy consumption. However, one of the most important cluster-based routing protocols for wireless sensor network has been proposed in [21]. The protocol has become the basis for several cluster-based routing protocols in the literature. The scheme operates in rounds and each round is sub divided into two phases, namely: setup phase and steady state phase. In the setup phase, each node produces a random number between 0 and 1.