Enterprise Application Integration (EAI) constitutes the cornerstone in enterprise IT landscapes that are characterized by heterogeneity and distribution. Starting from established Enterprise Integration Patterns (EIPs) such as Content-based Router and Aggregator, EIP compositions are built to describe, implement, and execute integration scenarios. The EIPs and their compositions must be correct at design and runtime in order to avoid functional errors or incomplete functionalities. However, current EAI system vendors use many of the EIPs as part of their proprietary integration scenario modeling languages that are not grounded on any formalism. This renders correctness guarantees for EIPs and their composition impossible. Thus this work advocates responsible EAI based on the formalization, implementation, and correctness of EIPs. For this, requirements on an EIP formalization are collected and based on these requirements an extension of db-net, i.e., timed db-net , is proposed, fully equipped with execution semantics. It is shown how EIPs can be realized based on timed db-nets and how the correctness of these realizations can be shown. Moreover, the simulation of EIP realizations based on timed db-nets is enabled which is essential for later implementation. The concepts are evaluated in many ways, including a proof-of-concept implementation and case studies. The EIP formalization based on timed db-nets constitutes the first step towards responsible EAI.