Partial offloading with stable equilibrium in fog-cloud environments using replicator dynamics of evolutionary game theory

Today, the use of fog computing is increasing due to the development of delay-sensitive applications in areas such as e-health, agriculture, and smart city management. In such applications, the use of partial offloading can provide better performance compared to full offloading. It means that part of the user's tasks can be offloaded to near fog devices and the rest can be performed locally for a better user experience. Unfortunately, here, users' selfishness to obtain fog device resources may lead to more complicated issues. There are various mathematical tools for modeling users' selfishness, the most common of which is game theory. Due to the NP-hard nature of the problem, the previous game-theoretical methods could not perform well when the number of users is large. Also, these methods require knowledge about other players. This paper proposes a partial offloading method based on replicator dynamics of evolutionary game theory. Here, the concept of player has been replaced by the strategy to increase scalability. Unlike previous research in which the complexity of the problem depends on the number of users, here, the number of strategies is a major concern. In addition, the proposed method does not require any hidden information from other users. It divides the population into local CPU cycles and offloaded CPU cycles, and then solves a dynamic equation to find out which of the two populations is growing. The results of solving the replicator equation followed by statistical analysis show that the proposed method has a remarkable performance improvement compared to the state-of-the-art methods. Our method, on average, results in a 17% energy saving compared to full local execution. It also reduces latency by 18% and 29% compared to full local and full offloading methods, respectively. Since the proposed method does not require hidden information about users, it can reduce the overhead by 15% compared to the local execution method.