“Mixed Criticality systems” seems to be a hot topic: just search on Google Scholar for “mixed criticality” and see how many papers have been published recently. It even became one of the main keywords in the latest IST Workprogramme of the EU.
A mixed criticality system is a system where different levels of certification are required for different subsystems. Some subsystems are considered highly-critical, and require a higher level of certification; some other parts of the system are less critical and can be subject to lower levels of certifications. The problem is that we must make sure that an error in the the less critical subsystems will not compromise certification of the high-criticality subsystems.
Concerning scheduling, one nice mathematical problem is how to make sure that high-criticality subsystems will be guaranteed correct under all circumstances, at the same time without under utilise system resources.
A high-criticality task is modelled with more than one worst-case computation times. For example, it can be modelled with two: one “typical” WCET, denoted as C-LO, is the one that the task will request most of the times. However, every once in a while, the task may require up to C-HI > C-LO.
Since in most cases the execution time of the high-critical task is low, than we can allocate the processing resources and admit low-criticality tasks assuming that the computation time is C-LO. However, when the computation time switches to C-HI, then we must still guarantee the high-criticality task (that has been certified), and drop some low-criticality task if necessary. In other words, we must guarantee the high-criticality task under all conditions; whereas, the low-criticality task can be dropped sometimes, when necessary.
As anticipated, many papers describe the problem and propose solutions. I suggest to start from the papers at UNC group, one of the most respect research group in real-time systems around. Here are a few links to start with (1) (2) (3).
I am also involved in the organization of a workshop on the topic, together with Laurent George. Here is the link to the web-page. Please consider submitting a paper, or just participating!