A parallel Poisson generator using parallel prefix

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 μ in average time complexity O([mμ/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 mμ, it achieves linear speedup when p is small and the average time complexity is O(log(mμ)) when p is O(mμ).