Coupling methods in connection with Poisson process approximation

Motivated by a simple probabilistic model for the radioactive decay, we show thatSerfling's [1978] approach to Poisson approximation using coupling techniques can in a natural way also be applied to Poisson process approximation. This provides at the same time uniform estimations for the deviation of a Markov-Bernoulli process from the approximating Poisson process with respect to the total variation distance. An application to quasirandom input queuing models is also given.