Microservice architecture is a service-oriented paradigm that enables the decomposition of cumbersome monolithic-based software systems. Using microservice design principles, it is possible to develop flexible, scalable, reusable, and loosely coupled software that could be containerized and deployed in a distributed edge/cloud environment. The flexible deployment of microservices in an edge environment increases system performance in terms due to dynamic service function placement and chaining possibly resulting in latency reduction, fault tolerance, scalability, efficient resource utilization, cost reduction, and energy consumption reduction. On the other hand, virtualization and containerization of microservices add processing and communication overheads. Therefore, to evaluate end-to-end microservices-based system performance, we need to have an end-to-end mathematical formulation of the overall microservice-based network system. Incorporating the virtualization overhead, here we provide end-to-end mathematical formulation considering system parameters: latency, throughput, computational resource usage, and energy consumption. We then evaluate the formulation in a testbed environment with the Microservice-based SDN (MSN) framework that decomposes the Software-defined Networking (SDN) controller in microservices with Docker Container. The final result validates the presented mathematical modeling of the system's dynamic behavior which can be used to design a microservice-based system.