  We have recently defined a weak Markovian bisimulation equivalence in an
integrated-time setting, which reduces sequences of exponentially timed
internal actions to individual exponentially timed internal actions having the
same average duration and execution probability as the corresponding sequences.
This weak Markovian bisimulation equivalence is a congruence for sequential
processes with abstraction and turns out to induce an exact CTMC-level
aggregation at steady state for all the considered processes. However, it is
not a congruence with respect to parallel composition. In this paper, we show
how to generalize the equivalence in a way that a reasonable tradeoff among
abstraction, compositionality, and exactness is achieved for concurrent
processes. We will see that, by enhancing the abstraction capability in the
presence of concurrent computations, it is possible to retrieve the congruence
property with respect to parallel composition, with the resulting CTMC-level
aggregation being exact at steady state only for a certain subset of the
considered processes.
