An algorithm and a methodology for the performability analysis of repairable distributed real-time systems are presented. The planning cycle of a real-time distributed system, which normally consists of several task invocations, is first identified. The performability distribution at the end of the planning cycle is determined by repeated convolutions of performability densities between task invocations. These convolution operations are efficiently carried out using the operational properties of Laguerre coefficients. The algorithm numerically determines both moments and distribution of performability in O(N/sub max//sup 3/), where N/sub max/ is the largest size of the state space between any task invocations. To illustrate the overall methodology, a simplified example of a radar system is analyzed, and the various performability measures are obtained using the algorithm.>

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.>

A time-scale decomposition (TSD) algorithm of a class of generalized stochastic Petri net (GSPN) models for performance evaluation of degradable multiprocessor systems is presented. The failure and repair rates in a multiprocessor system are an order of magnitude smaller than the rates of job arrival and completion; therefore, the GSPN models of these systems are decomposed into a hierarchical sequence of aggregated subnets, each of which is valid at a certain time scale. These smaller subnets are involved in isolation, and their solutions are combined to get the solution of the whole system. The algorithm is described step-by-step using a simple example. Then a large degradable multiprocessor system, which is intractable using conventional GSPN solution techniques, is analyzed. The complexity of the TSD algorithm is an order of magnitude smaller.>