Are there any stochastic models of non determinism in the rate of program execution?

Question

We know that typical operating systems and high level languages (especially those with garbage collection) cannot be used for real time operating systems. Java & jet engines don't mix, and consequently a lot of study has gone into researching and developing real time operating systems.

Is there any research as to exactly why a traditional operating system and high level garbage collecting language can't be used? I'm interested in any stochastic modelling that might have been done, rather than lots of words. So as a simple example, is there a mathematical model for the execution rate of say a simple FOR /NEXT loop on something like *nix + Java? Ideally this should refer to contemporary micro processors with all their associated speculative execution, interrupt handling and other modern optimisations like memory reclamation and parallel processing.

I would also extend this reference request to any models that might try to equate the mensuration of the execution rate of such a FOR /NEXT loop, with the Observer Effect as found in quantum mechanics.