A concept for the approximate steady-state analysis of non-Markovian processes is suggested, in which deterministically timed activities are allowed to take place concurrently. The approach works by mapping the actual process on a simplified process in which the deterministic timing is synchronized and the process can be solved by using an embedded Markov chain. In the simplified process the deterministic activities can be made faster or slower than in the actual process such that upper and lower bounds for the resulting state probabilities can be given. This is possible without state-space expansion and leads already to good results in the reported experiments. However, if the gap between the bounds is not sufficient, a phase expansion can be used, in which the synchronous approximation error is restricted to just one phase. The approach is explored for an M/D/2/K queuing system but is not restricted to it. Traditional expansion by phase-type distributions does not provide bounds.