7 Conclusion and Future Work
نویسندگان
چکیده
15] A. Cumani. ESP-A package for the evaluation of stochastic Petri nets with phase-type distributed transitions times. modeling of an automated manufacturing system with deterministic and stochastic Petri nets. net analysis of a replicated le system.mated generation and analysis of Markov reward models using Stochastic Reward Nets. 16 of (000111; 1), which is set to seven. Then, we can solve the embedded DTMC for steady state and obtain a steady-state probability vector ~ for the embedded process. The steady-state probability vector of the actual process is then obtained by weighting ~ according to the holding times, a well known result applicable to the steady-state solution of any semi-Markov process 8]: s = ~ s h s (P u2S ~ u h u) ?1. For transient analysis, the same idea can be applied, but in a much more restricted way. If, at step n, every state in S n] is such that the minimum time before a change of marking is k > 1, we can eeectively perform an embedding. In the modiied power method algorithm, this requires advancing n by k instead of just one step in the outermost loop and adjusting the increment of Y in statement 3 accordingly. It should be noted, however, that this situation is unlikely to occur, since the set S n] may contain many states s = (;), and, for each of them, the DTMC describing the ring time of each enabled transition t in must satisfy min n l 2 IN : Prf l] t = 0 j 0] t = t g > 0 o k: This is analogous to the requirement for an eecient application of adaptive uniformization 28] and, as stated in the introduction, it is unlikely to happen in general, especially for large values of F. We deened a class of discrete-time distributions which, when used to specify the ring time of the transitions in a stochastic Petri net, ensures that the underlying stochastic process is a DTMC. We then gave conditions under which the transient analysis of this DTMC can be performed even if the state space is innnite. In practice, though, the memory requirements might still be excessive, hence we explored some state-space reduction techniques. The implementation of a computer tool based on the DDP-SPN formalism is under way. In particular, algorithms for the eecient computation of the rows of the transition probability matrix, s; , are …
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