Time triggered methods provide deterministic behaviour suitable for critical real-time systems. The), perform less favourably, however if the arrival times of some activities are not known in advance, in particular if overload situations have to be anticipated. In many systems, the criticality of only a subset of activities justify the cost associated with the time triggered methods. In this paper we consider distributed systems where a subset of critical activities are handled in a time triggered fashion, via an offline schedule. At runtime, the arrival of aperiodic tasks may cause overload that demands to be handled in such a way that i) time triggered activities still meet all their original constraints, ii) execution of high-valued tasks are prioritised over tasks with lower value, iii) tasks can be quickly migrated to balance the overall system load. We give a precise formulation of overload detection and value based task rejection in the presence of offline scheduled tasks, and present a heuristic algorithm to handle overload. To benefit from the distributed setting, the overload handling includes an algorithm that integrates migration of rejected tasks with resource reclaiming and an acceptance test of newly arrived tasks. Simulation results underline the effectiveness of the presented approach.