Recycling random numbers in the stochastic simulation algorithm

Abstract

The stochastic simulation algorithm (SSA) was introduced by Gillespie and in a different form by Kurtz. Since its original formulation there have been several attempts at improving the efficiency and hence the speed of the algorithm. We briefly discuss some of these methods before outlining our own simple improvement, the recycling direct method (RDM), and demonstrating that it is capable of increasing the speed of most stochastic simulations. The RDM involves the statistically acceptable recycling of random numbers in order to reduce the computational cost associated with their generation and is compatible with several of the pre-existing improvements on the original SSA. Our improvement is also sufficiently simple (one additional line of code) that we hope will be adopted by both trained mathematical modelers and experimentalists wishing to simulate their model systems.