Distribution of random streams for simulation practitioners

Abstract

There is an increasing interest in the distribution of parallel random number streams in the high-performance computing community particularly, with the manycore shift. Even if we have at our disposal statistically sound random number generators according to the latest and thorough testing libraries, their parallelization can still be a delicate problem. Indeed, a set of recent publications shows it still has to be mastered by the scientific community. With the arrival of multi-core and manycore processor architectures on the scientist desktop, modelers who are non-specialists in parallelizing stochastic simulations need help and advice in distributing rigorously their experimental plans and replications according to the state of the art in pseudo-random numbers parallelization techniques. In this paper, we discuss the different partitioning techniques currently in use to provide independent streams with their corresponding software. In addition to the classical approaches in use to parallelize stochastic simulations on regular processors, this paper also presents recent advances in pseudo-random number generation for general-purpose graphical processing units. The state of the art given in this paper is written for simulation practitioners.

On parallel random number generation for accelerating simulations of communication systems

“…A comprehensive summary about generation methods for parallel RN streams has been given recently by Hill et al (2013). This section will give a brief overview and comments on some of the methods for generating multiple independent RN streams.…”

“…Correlations between the RN streams generated by following this approach are considered highly unlikely. As the parameter sets for the WELL and MT generator types have to be found by extensive search, parallelism by using this so-called Parametrization is also limited (Tian and Benkrid, 2009 Hill et al, 2013).…”

“…To a special degree, this research was driven by Pierre L'Ecuyer, Michael Mascagni, and others who investigated novel RNG approaches. For example, L'Ecuyer has formulated several key criteria for "good" RNGs: a long period, repeatable outputs, portability to different execution platforms, and the ability to split the output sequence into multiple independent blocks (what means they should implement an efficient jump-ahead strategy) and each block again into substreams with the leap frog approach (L'Ecuyer, 2007; L' Ecuyer and Panneton, 2005 Ecuyer and Simard, 2007) is considered the most comprehensive one and is preferred by many researchers (Salmon et al, 2011;Hill et al, 2013). A first requirement for a good parallel PRNG is that it also has to be a good sequential PRNG (Srinivasan et al, 2003).…”

“…A first requirement for a good parallel PRNG is that it also has to be a good sequential PRNG (Srinivasan et al, 2003). Obviously, when testing different substreams of one PRNG, it is mandatory to ensure that exactly the same substream can be outputted again to allow debugging and reproducibility of the test results (Hill et al, 2013).…”

“…Secondly, it is quite likely that the untreated output of a true RNG is biased. Therefore the output stream needs to be monitored continuously, and a bias correction is needed that is adjusted continuously (Hill et al, 2013). Thirdly, true RNs are not repeatable, and forbid re-executing a simulation several times with generating exactly the same output -a knock-out criterion for science in general.…”