We study joint optimization of service placement, request routing, and CPU sizing in a cooperative MEC system. The problem is considered from the perspective of the service provider (SP), which delivers heterogeneous MEC-enabled delay-sensitive services, and needs to pay for the used resources to the mobile network operators and the cloud provider, while earning revenue from the served requests. We formulate the problem of maximizing the SP's total profit subject to the computation, storage, and communication constraints of each edge node and end-to-end delay requirements of the services as a mixed-integer non-convex optimization problem, and prove it to be NP-hard. To tackle the challenges in solving the problem, we first introduce a design trade-off parameter for different delay requirements of each service, which maintains flexibility in prioritizing them, and transform the original optimization problem by the new delay constraints. Then, by exploiting a hidden convexity, we reformulate the delay constraints into an equivalent form. Next, to handle the challenge of the complicating (integer) variables, using primal decomposition, we decompose the problem into an equivalent form of master and inner sub-problems over the mixed and real variables, respectively. We then employ a cutting-plane approach for building up adequate representations of the extremal value of the inner problem as a function of the complicating variables and the set of values of the complicating variables for which the inner problem is feasible. Finally, we propose a solution strategy based on generalized Benders decomposition and prove its convergence to the optimal solution within a limited number of iterations. Extensive simulation results demonstrate that the proposed scheme significantly outperforms the existing mechanisms in terms of the SP's profit, cache hit ratio, running time, and end-to-end delay.

翻译：我们研究了协作移动边缘计算（MEC）系统中服务部署、请求路由与CPU分配的联合优化问题。该问题从服务提供商（SP）的视角展开，其提供异构的MEC支持的延迟敏感型服务，需向移动网络运营商和云服务商支付资源使用费，同时通过服务请求获取收益。我们将SP总利润最大化问题建模为混合整数非凸优化问题，约束条件包括各边缘节点的计算、存储和通信资源限制，以及服务的端到端延迟要求，并证明其为NP难问题。为解决求解中的挑战，我们首先针对每项服务的不同延迟需求引入设计折衷参数，以保持优先级分配的灵活性，并通过新的延迟约束转换原始优化问题。随后，利用隐凸性将延迟约束重构为等价形式。为处理复杂（整数）变量的挑战，我们采用原始分解法将问题分解为等价的主问题与内部子问题，分别对应混合变量与实数变量。进而采用割平面法，针对内部问题作为复杂变量函数时的极值及内部问题可行时复杂变量取值集合，构建充分近似表示。最终，我们提出基于广义Benders分解的求解策略，并证明其在有限迭代次数内收敛至最优解。广泛仿真结果表明，所提方案在SP利润、缓存命中率、运行时间及端到端延迟等指标上显著优于现有机制。