Converged networks support applications with completely different (real-time) requirements. The communication paradigms offered in converged networks are predominantly treated as separate entities from the perspective of traffic engineering, e.g., time-triggered traffic for closed-loop control systems, shaped traffic for multimedia-streaming applications, and best-effort traffic for non-time-critical IT applications. However, there are scenarios where applications benefit from considering time-triggered messages and non-time-triggered messages as complemental components of a single traffic flow. These applications have the property that time-triggered transmissions guarantee basic functionality (e.g., stability of a control system), and additional non-time-triggered transmissions improve the application's performance.

We present how to model these so-called complemental traffic flows for this type of application using a traffic metric for the description of the non-time-triggered traffic part. Furthermore, we show that complemental flows are suitable for traffic engineering by presenting two different approaches for the problem of optimized joint routing and scheduling in converged networks with mixed integer linear programming.

In our evaluations, we use an exemplary min-max objective for the joint routing and scheduling problem which yields an average reduction of the peak value of the traffic metric by 20-30\% over constraint-based approaches.