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 sliding 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, we 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 Lget
large, with T substantially bigger than L. We 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. We also develop an approximate relation between the two maximum window sizes. We apply the asymptotic results to develop approximations for the means and standard deviations of
the two maximum window contents. We apply computer simulation to evaluate
and refine these approximations.
