## 3 System Model and Framework  
### System Architecture  
Complexity in the IoT is higher than in WSNs, as it has a large number of objects and due to this reason it has a large scale. Dynamic routing (a routing scheme in which routes can be changed at any time during data transmission or routes are decided during the processing of data as proposed in [11, 13, 17, 63]) for WSN architectures is not suitable in large scale areas, e.g., in environment monitoring applications. The transmission of sensors is affected by many factors like air humidity, temperature and interference, so WSN architectures with dynamic routing are unusable for large scale networking. Tiny sensor nodes have constraints of low battery energy, low power and low memory and in large scale applications their processing requirements are increased. Sensor nodes require information regarding their location to be exchanged in dynamic routing. Consequently, nodes consume more power due to the increased overhead. That is why this type of routing is not applicable to the IoT. Moreover, network components deployed in the IoT are less mobile and their topology remains stable, so a dynamic routing configuration does not gain much over static routing. Considering the above factors we propose static and energy efficient routing for a scalable and complex IoT. We studied the effect of using our transmission algorithm over a thousand nodes deployed in a 200 and 300 m\({}^{2}\) area with different numbers of nodes and found that static routing is really suitable for scalable IoT applications. We have used the same tiered framework as used in [1], except for the relay layer which is not used in our framework, as can be seen in Figure 1. It presents the hierarchical network structure where all objects placed are static and follow the transmission based on static routing. Figure 1: Multi-tier Framework for IoT (CH: Cluster Heads; CCO: Cluster Coordinators; RN: Relay Nodes; NN: Normal Nodes). The lower layers consist of sensor nodes, cluster heads, relay nodes and cluster coordinators. The topmost layer is the convergence layer. This layer is comprised of base stations which are connected to the internet. In the lower layers, nodes sense the thing or the objects and transmit the data to the RN nodes. RNs pass the data to the CHs. To balance the load on the CHs and CCOs, CHs pass the data to the upper layer CCO which further hands over the data to the upper layer CCO and this process continues till the data is transmitted to the BS at the topmost layer. To conserve energy, nodes are not allowed to communicate with each other within the cluster and with the upper layer cluster. Locally, information is transmitted via RNs and communication with neighbor cluster is through the CHs and CCOs only. This deployment supports the energy efficient and scalable IoT. This type of deployment is general and can be used for any type of application environment monitoring, border surveillance, _etc._  
This scheme is flexible, provides scalability and hence can be easily managed. By the placement of IoT components above this framework, energy can be conserved in an efficient manner. As routing is static and simple, soon advantage of this layered scheme is that the various components of the IoT do not need complicated hardware and complex methods, which is very cost effective strategy. Let there be in the Euclidean plane two points u and v, and let the distance between them be \(d(u,v)\), the set of the local nodes within the cluster is denoted by NN1, the set of cluster coordinators is denoted by CC1, the set of relay nodes is denoted by RN1, the set of base stations is denoted by BS1, the set of CHs is denoted by CH1, the set of cluster ids is CLS_IDand the lower cluster is denoted by L_CLS and the upper cluster is denoted by U_CLS. A network of the IoT is denoted by G(N,V), where N is the set of all the nodes between the field and V is the set of wireless links among the nodes.