An open-loop window flow-control scheme regulates the flow into a system by allowing at most a specified window size W of flow in any interval of length L. The slidng window considers all subintervals of length L, while the jumping window considers consecutive disjoint intervals of length L. To better understand how these window control schemes perform for stationary sources, the authors describe for a large class of stochastic input processes the asymptotic behavior of the maximum flow in such window intervals over a time interval [0,T] as T and L get large, with T substantially bigger than L. They use strong approximations to show that when T>>L>>logT an invariance principle holds, so that the asymptotic behavior depends on the stochastic input process only via its rate and asymptotic variability parameters. In considerable generality, the sliding and jumping windows are asymptotically equivalent. The authors also develop an approximate relation between the two maximum window sizes. They apply the asymptotic results to develop approximations for the means and standard deviations of the two maximum window contents. The authors apply computer simulation to evaluate and refine these approximations.
