  Cloud and edge computing have been widely adopted in many application
scenarios. With the increasing demand of fast iteration and complexity of
business logic, it is challenging to achieve rapid development and continuous
delivery in such highly distributed cloud and edge computing environment. At
present, microservice-based architecture has been the dominant deployment
style, and a microservice system has to evolve agilely to offer stable Quality
of Service (QoS) in the situation where user requirement changes frequently.
Many research have been conducted to optimally re-deploy microservices to adapt
to changing requirements. Nevertheless, complex dependencies between
microservices and the existence of multiple instances of one single
microservice in a microservice system have not been fully considered in
existing works. This paper defines SPPMS, the Service Placement Problem in
Microservice Systems that feature complex dependencies and multiple instances,
as a Fractional Polynomial Problem (FPP) . Considering the high computation
complexity of FPP, it is then transformed into a Quadratic Sum-of-Ratios
Fractional Problem (QSRFP) which is further solved by the proposed greedy-based
algorithms. Experiments demonstrate that our models and algorithms outperform
existing approaches in both quality and computation speed.
