We address the problem of transient and steady-state analysis of stochastic discrete event systems which include concurrent activities with multiple time scales finite support distributions (and consequently non Markovian). Rather than computing an approximate distribution of the model (as done in previous methods), we develop an exact analysis of an approximate model. The design of this method leads to a uniform handling for the computation of the transient and steady-state behaviour of the model. We extend a previous result restricted to one time scale in order to handle different time scales. Furthermore, we show that some useful classes of non ergodic systems can be analyzed in an exact way with this method. We have evaluated our algorithms on standard queuing models benchmarks. Our results demonstrate that in most of the cases the solution of the approximate model converges quickly to the solution of the exact model, and in the difficult cases (e.g. an heavy load on the queue) our method is more robust than the previous ones.