In the Internet of Things (IoT) perceived applications of monitoring the states of the environment, a feasible technology is to use fog radio access networks (F-RANs) to alleviate the problems of long response time and cloud server bottlenecks in cloud computing. In response to the above problems, this work investigates the problem of minimizing the retrieval delay of IoT contents in F-RANs under the constraints of system resources. The problem is formulated as an integer linear programming (ILP) model. Then, a polynomial-time method with linear programming (LP) relaxation and rounding is proposed to approximate the optimal solution of the problem. Through proof, the method can obtain a feasible solution with a bounded approximation ratio in polynomial time. The conducted simulations validate that the obtained feasible solution is very close to the optimal one. On the other hand, when the system resources are not enough to meet the continuous growth of content retrieval and need to be expanded, this work further establishes an association relation between cached contents and system resources. Based on the above relation, the second method of expanding system resources with performance sensitivity is proposed to provide the service provider with an effective and economical expansion of system resources. It utilizes a predefined system parameter in balancing the trade-off between the approximation ratio to the optimal solution of the problem and the extended system resources. The solution obtained by the second method is also proved to have a bounded approximation ratio.
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