For description of dynamics of changes random loads of information flows we examine the stochastic model of Double Stochastic Poisson process which manages points of changes the random loads. A special case of a discrete distribution for the random intensity provides the following covariance property to the corresponding Double Stochastic Poisson subordinator for a sequence of the random loads. Such covariance exactly coincides with the covariance of the fractional Ornstein-Uhlenbeck process. Applying the Lamperti transform we obtain a self-similar random process with continuous time, stationary in the wide sense increments, and one dimensional distributions scaling the distribution of a term of the the initial subordinated sequence of the random loads. The Central Limit Theorem for vectors allows us to obtain in a limit, in the sense of convergence of finite dimensional distributions, the fractional Gaussian Brownian motion and the fractional Ornstein- Uhlenbeck process.