Asymptotics for open-loop window flow control. (1994)

• Record Type: Journal Article
• Authors: Berger, Arthur W.; Whitt, Ward
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 3(1994)
• Page Start: 337
• Page End: 356
• Publication Date: 1994
• Subjects: open-loop control -- traffic descriptor -- sliding window -- jumping window -- scan statistic -- strong approximations -- extreme values -- asymptotics; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000298
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : 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 L get large, with T substantially bigger than L . We use strong approximations to show that when T ≫ L ≫ log T 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.