Multi-tier computing can enhance the task computation by multi-tier computing nodes. In this paper, we propose a cell-free massive multiple-input multiple-output (MIMO) aided computing system by deploying multi-tier computing nodes to improve the computation performance. At first, we investigate the computational latency and the total energy consumption for task computation, regarded as total cost. Then, we formulate a total cost minimization problem to design the bandwidth allocation and task allocation, while considering realistic heterogenous delay requirements of the computational tasks. Due to the binary task allocation variable, the formulated optimization problem is nonconvex. Therefore, we solve the bandwidth allocation and task allocation problem by decoupling the original optimization problem into bandwidth allocation and task allocation subproblems. As the bandwidth allocation problem is a convex optimization problem, we first determine the bandwidth allocation for given task allocation strategy, followed by conceiving the traditional convex optimization strategy to obtain the bandwidth allocation solution. Based on the asymptotic property of received signal-to-interference-plus-noise ratio (SINR) under the cell-free massive MIMO setting and bandwidth allocation solution, we formulate a dual problem to solve the task allocation subproblem by relaxing the binary constraint with Lagrange partial relaxation for heterogenous task delay requirements. At last, simulation results are provided to demonstrate that our proposed task offloading scheme performs better than the benchmark schemes, where the minimum-cost optimal offloading strategy for heterogeneous delay requirements of the computational tasks may be controlled by the asymptotic property of the received SINR in our proposed cell-free massive MIMO-aided multi-tier computing systems.

翻译：多层级计算可通过多层级计算节点增强任务计算能力。本文提出一种部署多层级计算节点的无小区大规模多输入多输出辅助计算系统以提升计算性能。首先，我们研究了任务计算的计算延迟和总能耗，并将其视为总成本。随后，针对计算任务的实际异构延迟需求，建立以总成本最小化为目标的带宽分配与任务分配联合优化问题。由于存在二元任务分配变量，该优化问题非凸。为此，我们将原始优化问题解耦为带宽分配子问题和任务分配子问题分别求解。鉴于带宽分配问题为凸优化问题，我们首先在给定任务分配策略下确定带宽分配方案，进而采用传统凸优化策略获取带宽分配解。基于无小区大规模MIMO场景下接收信干噪比的渐近特性及带宽分配解，通过拉格朗日部分松弛法放松二元约束以处理异构任务延迟需求，构建对偶问题求解任务分配子问题。最后，仿真结果表明，所提任务卸载方案优于基准方案。在本文提出的无小区大规模MIMO辅助多层级计算系统中，面向异构计算任务时延需求的最小成本最优卸载策略可通过接收信干噪比渐近特性进行调控。