Design and analysis of vectorized Monte Carlo codes
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Date
1989
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Abstract
Vectorized Monte Carlo codes use a set of vectors, generally referred to as a stack in the literature, to hold the attribute values of the entities carrying out random walks. This paper presents schemes for optimizing the performance of stack processing in Monte Carlo codes and carries out their execution time analyses. The proposed four schemes are: (i) continuous inspection of the stack with no stack compression, (ii) continuous inspection of the stack with stack compression, (iii) periodical inspection of the stack with no stack compression, and (iv) periodical inspection of the stack with stack compression. The execution time analysis of the continuous schemes is carried out using some results from Order Statistics, and that of the periodical inspection schemes is carried out using some results from Markovian decision processes. Under some assumptions, one of them being that the time required for random walk computations is exponentially distributed, closed-form expressions for the expected execution time are obtained. The theoretical performance of the proposed schemes is illustrated and concluding remarks are given. Finally, the performance of the schemes is illustrated through vectorizing few Monte Carlo codes and running them on IBM 3090-180VF.
Keywords: Markovian decision processes, Monte Carlo codes, order statistics, parallel processing, supercomputing, vector processing