Cooperation between the fog and the cloud in mobile\udcloud computing environments could offer improved offloading\udservices to smart mobile user equipment (UE) with computation\udintensive tasks. In this paper, we tackle the computation offloading\udproblem in a mixed fog/cloud system by jointly optimizing\udthe offloading decisions and the allocation of computation resource,\udtransmit power and radio bandwidth, while guaranteeing\uduser fairness and maximum tolerable delay. This optimization\udproblem is formulated to minimize the maximal weighted cost\udof delay and energy consumption (EC) among all UEs, which\udis a mixed-integer non-linear programming problem. Due to\udthe NP-hardness of the problem, we propose a low-complexity\udsuboptimal algorithm to solve it, where the offloading decisions\udare obtained via semidefinite relaxation and randomization and\udthe resource allocation is obtained using fractional programming\udtheory and Lagrangian dual decomposition. Simulation results\udare presented to verify the convergence performance of our\udproposed algorithms and their achieved fairness among UEs, and\udthe performance gains in terms of delay, EC and the number of\udbeneficial UEs over existing algorithms.
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