asymptotics for open-loop window flow control

[摘要] An open-loop window flow-control scheme regulates the flow into a system by allowing at most a specified window sizeWof flow in any interval of lengthL. Thesliding windowconsiders all subintervals of lengthL, while thejumping windowconsiders consecutive disjoint intervals of lengthL. 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]asTandLget large, withTsubstantially bigger thanL. We use strong approximations to show that whenT≫L≫logTan 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.

[学科分类] 应用数学