The key operation to obtain stationary and transient solutions of transition systems described by Kronecker structured formalisms is the Vector-Descriptor product. This operation is usually performed with shuffling operations and matrices aggregations to reduce the floating point multiplications inside iterative methods. Due to the flexibility of the Split method treating Kronecker product terms, it is a natural alternative to decompose descriptors within parallel environments. The main problem is to define the correct task size to assign to each node and also the shared memory size, since sending a small task per time can lead to a larger communication overhead. In this paper we are investigating data partitioning strategies for a parallel solution of transition systems obtained from Kronecker descriptors using the Split algorithm.

The solution of Markovian models is usually nontrivial to be performed using iterative methods, so it is wellfitted to simulation approaches and high performance implementations. The Bootstrap simulation method is a novel simulation technique of Markovian models that brings a considerable improvement in the results accuracy, notwithstanding its higher computation cost when compared to other simulation alternatives. In this paper, we present three parallel implementations of the Bootstrap simulation algorithm, exploiting a multi-core SMP cluster. We discuss some practical implementation issues about processing and communication demands, as well as present an analysis of speedup and efficiency considering different models' sizes and simulation trajectory lengths. Finally, future works point out some improvements to achieve even better results in terms of accuracy.

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