Minimization of Weighted Bandwidth and Computation Resources of Fog Servers under Per-Task Delay Constraint
Xiumei Yang, Zening Liu, Yang Yang · 2018
Fog computing is seen as a promising approach to perform computation-intensive and latency-critical applications for mobile devices. Existing results mainly focus on power consumption or delay minimization problems which are both from the perspective of end devices. In this work, we further investigate the communication and computation resources minimization problem from the standpoint of the fog server operators instead. In practice, fog server operators must at first decide how many communication resources, e.g., bandwidth, and computation units should be deployed in order to satisfy various requirements from their serving devices. Meanwhile, the operators have to maximize their profits by balancing the cost of the deployed resources and devices' satisfaction. Motivated by such requirements, we formulate the problem as the minimization of the weighted bandwidth and computation resources with per-task delay requirement constraints. We prove that the optimization problem is convex and further derive important properties for the relationship between the required delay and the available resources. It indicates that there is an unachievable region for the completion time, where the task can not be completed within the required delay no matter how large the amount of communication bandwidth and the computation resources at the fog server is. We evaluate the performance of the feasible solutions for the mentioned problem through extensive numerical simulations and the numerical results have verified the analysis and the conclusions.