Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes

TL;DR

This paper introduces a generalized weak Markovian bisimulation that balances abstraction, compositionality, and exactness, enabling exact CTMC-level aggregation for concurrent processes under certain conditions.

Contribution

It extends previous weak Markovian bisimulation to concurrent processes, achieving a congruence with respect to parallel composition while maintaining exact CTMC aggregation for a subset of processes.

Findings

Achieves a tradeoff between abstraction, compositionality, and exactness.

Retrieves congruence property for parallel composition.

Provides exact CTMC aggregation for certain process subsets.

Abstract

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.