  Small cells with edge computing are densely deployed in 5G mobile networks to
provide high throughput communication and low-latency computation. The
flexibility of edge computation is empowered by the deployment of lightweight
container-based microservices. In this paper, we take the first step toward
optimizing the microservice management in small-cell networks. The prominent
feature is that each microservice consists of multiple image layers and
different microservices may share some basic layers, thus bringing deep
coupling in their placement and service provision. Our objective is to minimize
the expected total latency of microservice requests under the storage,
communication and computing constraints of the sparsely interconnected small
cell nodes. We formulate a binary quadratic program (BQP) with the
multi-dimensional strategy of the image layer placement, the access selection
and the task assignment. The BQP problem is then transformed into an ILP
problem, and is solved by use of a novel sphere-box alternating direction
multipliers method (ADMM) with reasonable complexity $O(q^{4})$, where $q$ is
the number of variables in the transformed problem. Trace-driven experiments
show that the gap between our proposed algorithm and the optimal is reduced by
35$\%$ compared with benchmark algorithms.
