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In the Internet of things (IoT) (Hanes et al., 2018), not only computers like servers and clients but also millions of sensor and actuator devices are interconnected in networks. In the cloud computing model (Creeger, 2009), data collected by sensors is sent to servers and processed by application processes on the servers. Here, networks are congested to transmit the huge volume of sensor data and servers are also overloaded to process the sensor data in realtime manner. The FC (Fog Computing) model (Rahmani et al., 2018) is proposed to reduce the communication and processing traffic to handle sensor data in the IoT. In the FC model, processing modules, i.e. subprocesses of an application process are distributed to not only servers but also fog nodes. A fog node processes sensor data and sends the output data obtained by processing the data to another fog node. On receipt of output data from fog nodes, a fog node further processes the data and sends the processed output data to other fog nodes. Thus, since subprocesses are performed on not only servers but also fog nodes and only processed sensor data is transmitted in networks, the server and network traffic can be reduced.
Since the IoT is so scalable that millions of nodes are interconnected, it is critical to reduce the electric energy consumed by fog nodes and servers. The power consumption models of a computer are proposed to show the electric power [W] to be consumed by the computer to perform types of application processes (Dilawaer et al., 2018a; Dilawaer et al., 2018b; Enokido et al., 2010; Enokido et al., 2011; Enokido et al., 2014; Kataoka et al., 2017). In order to reduce the energy consumption and execution time of fog nodes and servers, the TBFC (Tree-Based FC) model (Oma et al., 2018a; Oma et al., 2018b; Oma et al., 2018d) is proposed. Here, an application process to handle sensor data is assumed to be linear, i.e. a sequence of subprocesses. Fog nodes are hierarchically structured in a height-balanced tree where a same subprocess is performed on fog nodes at each level. Nodes at a root level and a bottom level show a cluster of servers and edge nodes which communicate with sensors and actuators, respectively. Sensors first send data to edge nodes. Each edge node generates output data by processing the input data and sends the output data to a parent fog node (Oma et al., 2018a). Thus, each fog node receives input data from child nodes and sends processed output data to a parent node.
In addition to energy-efficiently and performance-efficiently realizing the FC model, it is critical to make fog nodes tolerant of faults. In order to be tolerant of node stop-faults, the FTBFC (Fault-tolerant TBFC) (Oma et al., 2018c; Oma et al., 2019a) and MFTBFC (Modified FTBFC) (Oma et al., 2019b; Oma et al., 2019c) models and the subprocess transmission strategy (Oma et al., 2019c) are proposed.