A parallel Poisson generator using parallel prefix

Abstract

In this paper, we use the renewal theory to develop a Poisson random number algorithm without restart. A parallel Poisson random number generator is designed based on this algorithm and prefix computation. This generator iteratively produces m Poisson random numbers with mean mu in average time complexity O([m mu/n]f(n, p)) on EREW PRAM, where f(n,p) is the time for computing an n-element parallel prefix on p processors in each iteration, assuming that parallel uniform random numbers can be generated at the rate of one number per unit time per processor. If n is selected near m mu, it achieves linear speedup when p is small and the average time complexity is O(log(m mu)) when p is O(m mu).