A Game-Theoretic Approach for Cost-Effective Multicast Routing in the Internet of Things

Abstract

Internet of Things (IoT) devices have enabled communications in resource-limited computing environments. Sensor nodes from the multiple IoT devices collectively work for many applications, such as disaster management, border security management, smart farming, smart cities, etc. In such applications, the data from a single source node is often destined for multiple nodes. Multicast communication is preferred over unicast or broadcast communication for such applications, as multicast uses fewer resources. Efficient construction of the multicast tree leads to cost-effective multicast transmission. This article introduces a path selection game (PSGame), a game-theoretic approach that formulates the construction problem of the least-cost multicast tree as a potential game. Our proposed path selection algorithm (PSA) quickly converges to the pure Nash equilibrium (PNE), bringing the least cost multicast tree. Our findings show that the overhead incurred in terms of energy consumption and delay is minimal in the proposed algorithm compared to other mechanisms. The theoretical analysis proves that the proposed algorithm quickly converges to PNE in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n.r_{\max })$ </tex-math></inline-formula> steps. It also proves that the cost ratio between the proposed solution and the centralized optimum will be bounded by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log (n)$ </tex-math></inline-formula> . The numerical analysis substantiates the theoretical analysis.