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Time Scale Decomposition of a Class of Generalized Stochastic Petri Net Models
June 1989 (vol. 15 no. 6)
pp. 809-820

A time-scale decomposition (TSD) algorithm of a class of generalized stochastic Petri net (GSPN) models of systems comprising activities whose duration differ by orders of magnitude is presented. The GSPN model of a system can be decomposed into a hierarchical sequence of aggregated subnets, each of which is valid at a certain time scale. These smaller subnets are solved in isolation and their solutions are combined to get the solution of the whole system. A degradable multiprocessor system which would be intractable using conventional techniques, is analyzed using TSD. The complexity of the TSD algorithm can be orders of magnitude smaller without any significant loss in the accuracy of the result. In general, the error due to aggregation is proportional to the maximum degree of coupling between aggregates. An expression of the error due to aggregation is also given in terms of the ratio of fast and slow transitions in the GSPN model. The algorithm is easy to use and can be easily automated.

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Index Terms:
generalized stochastic Petri net models; time-scale decomposition; GSPN model; hierarchical sequence; aggregated subnets; degradable multiprocessor system; complexity; TSD algorithm; aggregation; coupling; slow transitions; multiprocessing systems; performance evaluation; Petri nets; stochastic processes
Citation:
H.H. Ammar, S.M.R. Islam, "Time Scale Decomposition of a Class of Generalized Stochastic Petri Net Models," IEEE Transactions on Software Engineering, vol. 15, no. 6, pp. 809-820, June 1989, doi:10.1109/32.24734
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