Example: The stationary Poisson process has a constant rate λ > 0 of customer arrivals. This means the interarrival time A between two consecutive customers is an exponential random variable with the cumulative distribution function A(t) = 1 − e. In order to generate the times of arrivals t1, t2, . . . of customer 1, 2, . . . starting from time t0, we use the inverse transform A−1 recursively.