Mobile-edge computing (MEC) has recently emerged as a cost-effective paradigm to enhance the computing capability of hardware-constrained wireless devices (WDs). In this paper, we first consider a two-user MEC network, where each WD has a sequence of tasks to execute. In particular, we consider task dependency between the two WDs, where the input of a task at one WD requires the final task output at the other WD. Under the considered task-dependency model, we study the optimal task offloading policy and resource allocation (e.g., on offloading transmit power and local CPU frequencies) that minimize the weighted sum of the WDs’ energy consumption and task execution time. The problem is challenging due to the combinatorial nature of the offloading decisions among all tasks and the strong coupling with resource allocation. To tackle this problem, we first assume that the offloading decisions are given and derive the closed-form expressions of the optimal offloading transmit power and local CPU frequencies. Then, an efficient bi-section search method is proposed to obtain the optimal solutions. Furthermore, we prove that the optimal offloading decisions follow an one-climb policy, based on which a reduced-complexity Gibbs Sampling algorithm is proposed to obtain the optimal offloading decisions. We then extend the investigation to a general multi-user scenario, where the input of a task at one WD requires the final task outputs from multiple other WDs. Numerical results show that the proposed method can significantly outperform the other representative benchmarks and efficiently achieve low complexity with respect to the call graph size.

中文翻译：

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具有用户间任务依赖性的移动边缘计算中的最佳任务卸载和资源分配

移动边缘计算 (MEC) 最近已成为增强硬件受限无线设备 (WD) 计算能力的一种经济高效的范例。在本文中，我们首先考虑一个双用户 MEC 网络，其中每个 WD 都有一系列要执行的任务。特别地，我们考虑了两个 WD 之间的任务依赖性，其中一个 WD 的任务输入需要另一个 WD 的最终任务输出。在考虑的任务依赖模型下，我们研究了使 WD 的能量消耗和任务执行时间的加权和最小化的最佳任务卸载策略和资源分配（例如，卸载传输功率和本地 CPU 频率）。由于所有任务之间卸载决策的组合性质以及与资源分配的强耦合，该问题具有挑战性。为了解决这个问题，我们首先假设卸载决策是给定的，并推导出最优卸载发射功率和本地 CPU 频率的闭式表达式。然后，提出了一种有效的二分搜索方法来获得最优解。此外，我们证明了最优卸载决策遵循单爬策略，在此基础上提出了一种降低复杂度的吉布斯采样算法以获得最优卸载决策。然后，我们将调查扩展到一般的多用户场景，其中一个 WD 的任务输入需要来自多个其他 WD 的最终任务输出。数值结果表明，所提出的方法可以显着优于其他代表性基准，并有效地实现了调用图大小的低复杂度。