Reliable random number generators are essential for stochastic simulation and for many other applications. In parallel computing environments, we need multiple streams of random numbers that can run independently of each other. This tutorial talk surveys the state of the art on the design and implementation of random number generators for simulation, with an emphasis on the production of multiple streams and substreams of random numbers. Different approaches are discussed, including the classical recurrence-based algorithmic generators, as well as the more recent counter-based generators and dynamically splittable generators, which permit one to create (not only run) the muliple streams in parallel. We also review the basic quality criteria for good random number generators in general, and their theoretical and empirical testing. Finally, we point out issues that would require further study and software that we still miss.
Pierre L'Ecuyer is a Professor in the Département d'Informatique et de Recherche Opérationnelle (DIRO), at Université de Montréal, Canada. He is a member of CIRRELT and GERAD research centers. He held a Canada Research Chair in Stochastic Simulation and Optimization for 2004–2017 and an Inria International Chair (at Inria-Rennes, France) for 2013–2018. His main research interests are random number generation, quasi-Monte Carlo methods, variance reduction, sensitivity analysis and optimization, and stochastic simulation in general. He has published about 300 scientific articles, developed stochastic simulation software, gave nearly 400 presentations at conferences, research centers, and universities, and served as a referee for 172 different scientific journals. He received the Lifetime Professional Achievement Award from the INFORMS Simulation Society in 2020, Computer Science Canada Lifetime Achievement Award in 2019, ACM SIGSIM Distinguished Contributions Award in 2016, Canadian Operational Research Society Award of Merit in 2014, the INFORMS Simulation Society Distinguished Service Award in 2011, and the INFORMS Simulation Society Outstanding Research Publication Award three times, in 1999, 2009, and 2018.
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Matthieu Boileau et Benoît Fabrèges
