  Reliability in terms of functional properties from the safety-liveness
spectrum is an indispensable requirement of low-level operating-system (OS)
code. However, with evermore complex and thus less predictable hardware,
quantitative and probabilistic guarantees become more and more important.
Probabilistic model checking is one technique to automatically obtain these
guarantees. First experiences with the automated quantitative analysis of
low-level operating-system code confirm the expectation that the naive
probabilistic model checking approach rapidly reaches its limits when
increasing the numbers of processes. This paper reports on our work-in-progress
to tackle the state explosion problem for low-level OS-code caused by the
exponential blow-up of the model size when the number of processes grows. We
studied the symmetry reduction approach and carried out our experiments with a
simple test-and-test-and-set lock case study as a representative example for a
wide range of protocols with natural inter-process dependencies and long-run
properties. We quickly see a state-space explosion for scenarios where
inter-process dependencies are insignificant. However, once inter-process
dependencies dominate the picture models with hundred and more processes can be
constructed and analysed.
