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The set of executing tasks in modern hard real time systems may change during system execution. This change, called scenario change, may lead to a transient overload situation due to the interference of different task set executions, thus necessitating timing requirement verification. Previously developed approaches analyzing response times across scenario changes are limited to strict periodic task event models and restricted to uniprocessor systems, while existing methods adapted for the analysis of distributed systems are not suitable for the analysis across scenario changes. In this paper, we eliminate the restrictions concerning task event models and present a scheduling analysis methodology allowing response time calculation across a scenario change for multi-scenario distributed systems.