The term Internet of Things (IoT) denotes a communication network, where various Things are interconnected using novel scenario-specific Internet technologies and predefined customizable semantics. Industry 4.0 aims at enabling a globally networked production, with the use of IoT as a crucial concept. Since production systems tend to be technically and organizationally heterogeneous, distributed at different locations, and associated with large amounts of data, communication and information processing platforms that provide confidentiality, integrity, availability (CIA rules), access control, and privacy are needed. In this contribution, we introduce a concept for designing and operating heterogeneous and spatially distributed industrial systems with Digital Twins, connected via an IoT communication infrastructure, the Smart Systems Service Infrastructure (S3I). By demonstrating an industrial use case with our concept, it is proven that the S3I can be used as a cross-domain solution for the interconnection of devices in a distributed production scenario.