Solving analytical structured formalisms in parallel using slice algorithm
Resumen
Analytical modeling can be used to predict performance, detect unexpected behavior and evaluate strategies in order to improve systems. In the context of modeling computational environments, a multitude of analytical structured modeling formalisms, such as Stochastic Automata Networks (SAN), is becoming popular since they provide high level abstractions and modularity. Indeed, in order to obtain performance estimations of a given SAN model, it is necessary to perform multiple matrix-vector multiplications. In structured formalisms, such as SAN, the matrix-vector multiplication is not presented in the usual format xA, since matrix A is replaced by an algebraic expression Q (called Markovian Descriptor or just descriptor, for short) due to modularity. The original multiplication is then replaced by a vector-descriptor multiplication (VDM), letting some space for algebraic improvements. Mainly, there are two algorithms that implement the VDM: shuffle and slice. In previous works, a parallel version of shuffle was proposed. It presented good results in terms of memory allocation but tasks are hard to split and hence compromises its scalability. The slice algorithm is based on an algebraic property that can, since its name says, split the VDM in many independent operations. The goal of this work is to underline a high performance version of the slice to check the scalability of this algorithm.
Palabras clave
Parallel applications, Kronecker/markovian descriptor, Structured analytical formalisms, Stochastic automata networks
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