  In this paper, we face the problem of simulating discrete random variables
with general and varying distributions in a scalable framework, where fully
parallelizable operations should be preferred. The new paradigm is inspired by
the context of discrete choice models. Compared to classical algorithms, we add
parallelized randomness, and we leave the final simulation of the random
variable to a single associative operation. We characterize the set of
algorithms that work in this way, and those algorithms that may have an
additive or multiplicative local noise. As a consequence, we could define a
natural way to solve some popular simulation problems.
