Conclusion

From the previous sections we conclude that almost all pseudorandom number generators used in simulations are linear methods. These PRNGs allow an easy theoretical analysis based on the linear structure of $s$-dimensional overlapping tuples. A disadvantage of linear methods is their weakness with respect to splitting, which restricts the use of these methods in parallel simulations. Previous tests are necessary, if subsequences of a linear generator are used for a particular simulation problem.

Finally we want to note that inversive pseudorandom number generators guarantee the absence of lattice structures [55,56,58,88,184,186]. Especially explicit inversive congruential PRNGs are very robust with respect to splitting their output sequences into subsequences and the splitting procedure is easy to handle [57,70,183,185]. Inversive generators are significantly slower than LCGs. Nevertheless, these generators provide substantially different PRNs to control simulation results obtained by linear methods.