Abstract
This paper proposes a novel abstraction technique based on Erlang’s method of stages for continuous-time Markov chains (CTMCs). As abstract models Erlang-k interval processes are proposed where state residence times are governed by Poisson processes and transition probabilities are specified by intervals. We provide a three-valued semantics of CSL (Continuous Stochastic Logic) for Erlang-k interval processes, and show that both affirmative and negative verification results are preserved by our abstraction. The feasibility of our technique is demonstrated by a quantitative analysis of an enzyme-catalyzed substrate conversion, a well-known case study from biochemistry.
The research has been partially funded by the DFG Research Training Group 1298 (AlgoSyn), the Swiss National Science Foundation under grant 205321-111840 and the EU FP7 project Quasimodo.
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Katoen, JP., Klink, D., Leucker, M., Wolf, V. (2008). Abstraction for Stochastic Systems by Erlang’s Method of Stages. In: van Breugel, F., Chechik, M. (eds) CONCUR 2008 - Concurrency Theory. CONCUR 2008. Lecture Notes in Computer Science, vol 5201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85361-9_24
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