To deliver high performance and reliability to the mobile users in accessing mobile cloud services, the major interest is currently given to the integration of centralized cloud computing and distributed edge computing infrastructures. In such a heterogeneous network ecosystem, multiple cloudlets from different service providers coexist. However, to meet the stringent latency requirements of computation-intensive and mission-critical applications, overloaded cloudlets can offload some of the incoming job requests to their relatively under-loaded neighboring cloudlets. In this paper, we propose a novel economic and non-cooperative game-theoretic model for load balancing among competitive cloudlets. This model aims to maximize the utilities of all the competing cloudlets while meeting the end-to-end latency of the users. We characterize the problem as a generalized Nash equilibrium problem and investigate the existence and uniqueness of a pure-strategy Nash equilibrium. We design a variational inequality based algorithm to compute the pure-strategy Nash equilibrium. We show that all the competing cloudlets are able to maximize their utilities by employing our proposed Nash equilibrium computation offload strategy in both under-and overloaded conditions. We also show through numerical evaluations that our load balancing model outperforms some of the existing game-theoretic load balancing frameworks, especially in a highly overloaded condition.INDEX TERMS Cloudlet computing, non-cooperative load balancing, generalized Nash equilibrium, variational inequality.

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The study of how spin interacts with lattice vibrations and relaxes to equilibrium provides unique insights into its chemical environment and the relation between electronic structure and molecular composition. Despite its importance for several disciplines, ranging from magnetic resonance to quantum technologies, a convincing interpretation of spin dynamics in crystals of magnetic molecules is still lacking due to the challenging experimental determination of the correct spin relaxation mechanism. We apply ab initio spin dynamics to a series of 12 coordination complexes of Co 2+ and Dy 3+ ions selected among ∼240 compounds that largely cover the literature on single-molecule magnets and well represent different regimes of spin relaxation. Simulations reveal that the Orbach spin relaxation rate of known compounds mostly depends on the ions' zero-field splitting and little on the details of molecular vibrations. Raman relaxation is instead found to be also significantly affected by the features of low-energy phonons. These results provide a complete understanding of the factors limiting spin lifetime in single-molecule magnets and revisit years of experimental investigations by making it possible to transparently distinguish Orbach and Raman relaxation mechanisms.

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