Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distribution
Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distribution
复制标题
具有泊松开/关远程依赖源和一般服务时间分布的队列的大流量限制定理
DOI：
10.1007/s10255-012-0190-2
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发表时间：
2011-05
影响因子：
0.8
通讯作者：
Dai, Wanyang
中科院分区：
文献类型：
--
作者：
Dai, Wanyang
在互联网环境中，一个链路的流量流通常是通过基于ON/OFF源的叠加来建模的。在特定源的每次开通期间，数据包根据泊松过程到达，数据包大小（因此服务时间）可以大致分布。本文建立了大流量限制定理，为先进先出（FIFO）和节省工作服务原则下的系统提供了合适的近似，该定理表明，当ON- and - off周期长度均为轻尾时，缩放后的队列长度序列和工作负载过程弱收敛于短距离依赖的反射高斯过程，当ON- and/or - off周期长度为重尾且方差无穷大时，当叠加源的数量趋于无穷大时，根据尺度的选择，序列弱收敛到反映分数布朗运动（FBMs）或某种类型的远程依赖反映高斯过程。当源数量足够大时，序列表现出类似状态空间坍缩的性质，这是对M/M/1排队系统的利特尔定律的一种扩展。证明近似的理论是基于适当的繁忙交通条件，这本质上意味着当输入源的数量趋于无穷大时，服务率接近到达率。
In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service times) can be generally distributed. In this paper, we establish heavy traffic limit theorems to provide suitable approximations for the system under first-in first-out (FIFO) and work-conserving service discipline, which state that, when the lengths of both ON- and OFF-periods are lightly tailed, the sequences of the scaled queue length and workload processes converge weakly to short-range dependent reflecting Gaussian processes, and when the lengths of ON- and/or OFF-periods are heavily tailed with infinite variance, the sequences converge weakly to either reflecting fractional Brownian motions (FBMs) or certain type of longrange dependent reflecting Gaussian processes depending on the choice of scaling as the number of superposed sources tends to infinity. Moreover, the sequences exhibit a state space collapse-likeproperty when the number of sources is large enough, which is a kind of extension of the well-known Little’s law for M/M/1 queueing system. Theory to justify the approximations is based on appropriate heavy traffic conditions which essentially mean that the service rate closely approaches the arrival rate when the number of input sources tends to infinity.
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DOI：
10.1109/infcom.2002.1019347
发表时间：
2002-11
期刊：
Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies
影响因子：
--
作者：
K. Ramanan;Jin Cao
通讯作者：
K. Ramanan;Jin Cao
影响因子：
1.2
作者：
K. Dȩbicki;Z. Palmowski
通讯作者：
K. Dȩbicki;Z. Palmowski
DOI：
10.1109/90.554723
发表时间：
1997-02
期刊：
IEEE/ACM Trans. Netw.
影响因子：
--
作者：
W. Willinger;M. Taqqu;R. Sherman;D. V. Wilson
通讯作者：
W. Willinger;M. Taqqu;R. Sherman;D. V. Wilson
影响因子：
1.2
作者：
J. Dai;W. Dai
通讯作者：
J. Dai;W. Dai
DOI：
10.2307/3612158
发表时间：
1970-05
期刊：
The Mathematical Gazette
影响因子：
--
作者：
Patrick Billingsley
通讯作者：
Patrick Billingsley