In this work we study a natural family of admission control policies which keep the associated scaled cumulative workload input asymptotically close to a pre- specified linear trajectory, uniformly over time.

Under such admission control policies and with natural assumptions on arrival distributions, suitably scaled and centered cumulative workload input processes are shown to converge weakly in the path space to the solution of a $d$- dimensional stochastic differential equation (SDE) driven by a Gaussian process. It is shown that the admission control policy achieves moment stabilization in that the second moment of the solution to the SDE (averaged over the d- stations) is bounded uniformly for all times. In one special case of control policies, as time approaches infinity, we obtain a fractional version of a stationary Ornstein-Uhlenbeck process that is driven by fractional Brownian motion with Hurst parameter H>1/2.