Distributed software architecture is composed of multiple interacting modules, or components. Deploying such software consists in installing them on a given infrastructure and leading them to a functional state. However, since each module has its own life cycle and might have various dependencies with other modules, deploying such software is a very tedious task, particularly on massively distributed and heterogeneous infrastructures. To address this problem, many solutions have been designed to automate the deployment process. In this paper, we introduce Madeus, a component-based deployment model for complex distributed software. Madeus accurately describes the life cycle of each component by a Petri net structure, and is able to finely express the dependencies between components. The overall dependency graph it produces is then used to reduce deployment time by parallelizing deployment actions. While this increases the precision and performance of the model, it also increases its complexity. For this reason, the operational semantics needs to be clearly defined to prove results such as the termination of a deployment. In this paper, we formally describe the operational semantics of Madeus, and show how it can be used in a use-case: the deployment of a real and large distributed software (i.e., OpenStack).