Context: With the increasing popularity of microservices for software application development, businesses are migrating from monolithic approaches towards more scalable and independently deployable applications using microservice architectures. Each microservice is designed to perform one single task. However, these microservices need to be composed together to communicate and deliver complex system functionalities. There are two major approaches to compose microservices, namely Choreography and Orchestration. Microservice compositions are mainly built around business functionalities, therefore businesses need to choose the right composition style that best serves their needs. Hence, this research uses existing complexity metrics from the software engineering and business process modeling domains on small, mid-sized, and end-to-end e-commerce scenarios to analyze and compare the level of complexity of microservice Orchestration and Choreography using Business Process Modeling Notation (BPMN).

Objective: Comparing the complexity of the two leading composition techniques on small, mid-sized, and end-to-end e-commerce scenarios, using complexity metrics from the software engineering and business process literature. More specifically, we use the metrics to assess the complexity of BPMN-based models representing the abovementioned e-commerce scenarios.

Method: This research follows a five-step process for conducting a Design Science Research (DSR) methodology to define, develop and evaluate BPMN-based models for microservice compositions.

Results: A series of BPMN workflows are designed as artifacts to investigate microservice Choreography and Orchestration. The results derived from the complexity evaluation of our proposed models show a higher level of complexity in orchestrating microservices for e-commerce applications given the number of services used in modeling Orchestration compared to Choreography.

Conclusion: This research uncovers insights on modeling microservice Choreography and Orchestration and discusses the impacts of complexity on the modifiability and understandability of the proposed models. Keywords: Microservice, Microservice Composition, Choreography, Orchestration, Complexity Metric, BPMN.