We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that minimise expected cost of reaching a given set of target states for a given cost function . We show that under mild assumptions, optimal values of parameters can be efficiently approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters . Even though the translation is theoretically efficient, we also provide heuristics that further decreases the size of the MDP depending on properties of the continuous-time model .
We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that , for a given cost function, minimise expected total cost incurred before reaching a given set of target states . We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters .
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minimise expected cost of
, for a given cost function, minimise expected total cost incurred before
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for a given cost function
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efficiently
effectively
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. Even though the translation is theoretically efficient, we also provide heuristics that further decreases the size of the MDP depending on properties of the continuous-time model