Multiple and Replicated Random Walkers Analysis for Service Discovery in Fog Computing IoT Environments

The multiple random walkers mechanism is revisited in this paper for service discovery purposes considering modern dynamic network environments like the Internet of Things (IoT), where there is a need for certain services (e.g., virtual network functions) to be available to the end users through fog computing devices. Network coverage is analytically investigated here considering multiple random walkers in soft random geometric graph topologies of various densities. It is shown that as the number of random walkers increases, then coverage linearly increases in the considered topologies. The analytical findings of this work are shown to be in accordance with other results in the literature (e.g., coverage under multiple random walkers for fully connected network topologies). Moreover, for certain coverage and time constraints (i.e., the minimum fraction of network nodes to be covered within a certain time period that is of practical importance in the considered environment), the required minimum number of random walkers satisfying these constraints is also analytically derived. A replication mechanism that allows random walkers to replicate themselves after a fixed number of time steps is also analytically investigated here with respect to coverage for various topology densities. Simulation results demonstrate the effectiveness of multiple random walkers for service discovery purposes in the considered fog computing IoT environment and support the claims and expectations of the analysis for both the multiple random walkers and the replicated multiple random walkers mechanism.