As software may be used by multiple users, caching popular software at the wireless edge has been considered to save computation and communications resources for mobile edge computing (MEC). However, fetching uncached software from the core network and multicasting popular software to users have so far been ignored. Thus, existing design is incomplete and less practical. In this paper, we propose a joint caching, computation and communications mechanism which involves software fetching, caching and multicasting, as well as task input data uploading, task executing (with non-negligible time duration) and computation result downloading, and mathematically characterize it. Then, we optimize the joint caching, offloading and time allocation policy to minimize the weighted sum energy consumption subject to the caching and deadline constraints. The problem is a challenging two-timescale mixed integer nonlinear programming (MINLP) problem, and is NP-hard in general. We convert it into an equivalent convex MINLP problem by using some appropriate transformations and propose two low-complexity algorithms to obtain suboptimal solutions of the original non-convex MINLP problem. Specifically, the first suboptimal solution is obtained by solving a relaxed convex problem using the consensus alternating direction method of multipliers (ADMM), and then rounding its optimal solution properly. The second suboptimal solution is proposed by obtaining a stationary point of an equivalent difference of convex (DC) problem using the penalty convex-concave procedure (Penalty-CCP) and ADMM. Finally, by numerical results, we show that the proposed solutions outperform existing schemes and reveal their advantages in efficiently utilizing storage, computation and communications resources.

中文翻译：

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移动边缘计算的联合优化软件缓存、计算卸载和通信资源分配

由于软件可能被多个用户使用，因此考虑在无线边缘缓存流行的软件，以节省移动边缘计算 (MEC) 的计算和通信资源。然而，迄今为止，从核心网络获取未缓存的软件以及向用户多播流行软件都被忽视了。因此，现有的设计是不完整的并且不太实用。在本文中，我们提出了一种联合缓存、计算和通信机制，涉及软件获取、缓存和多播，以及任务输入数据上传、任务执行（具有不可忽略的持续时间）和计算结果下载，并对其进行数学表征。 . 然后，我们优化联合缓存、卸载和时间分配策略，以最小化受缓存和期限约束的加权总和能量消耗。该问题是一个具有挑战性的双时间尺度混合整数非线性规划 (MINLP) 问题，并且通常是 NP-hard 问题。我们通过使用一些适当的变换将其转换为等效的凸 MINLP 问题，并提出两种低复杂度的算法来获得原始非凸 MINLP 问题的次优解。具体来说，第一个次优解是通过使用乘法器的共识交替方向法（ADMM）解决一个松弛的凸问题，然后对其最优解进行适当的取整得到的。通过使用惩罚凸凹过程 (Penalty-CCP) 和 ADMM 获得凸 (DC) 问题的等效差的驻点，提出了第二个次优解决方案。最后，通过数值结果，