On the Influence of Fog Colonies Partitioning in Fog Application Makespan

This paper presents a study of the use of network centrality indices as suitable indicators to determine the partitioning of fog colonies. Fog colonies have been used previously to enable a two level (inter and intra colony) resource management for the fog service placement problem. We propose selecting the nodes with highest values, which indicate the node importance, as the colony controllers. The remaining devices are subordinated to the closest controllers. We studied six centrality indices in three network topologies and two architecture sizes. The fog applications are designed as a set of interoperated services which makespan is increased when services are allocated in different colonies, or colonies have highest intra or inter distances. Consequently, we considered the network distance as indicator of the application makespan. The results showed that the smaller network distances was obtained with the Betweenness centrality index and a Barabasi-Albert network topology. It was also observed that the network distance only has significant differences when the colony size is varied between 1 and 20.