A Poisson limit for buffer overflow probabilities
A Poisson limit for buffer overflow probabilities
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DOI：
10.1109/infcom.2002.1019347
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发表时间：
2002-11
期刊：
影响因子：
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通讯作者：
K. Ramanan;Jin Cao
中科院分区：
文献类型：
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作者：
K. Ramanan;Jin Cao
高速网络设计的一个关键准则是缓冲区内容超过给定阈值的概率。我们将n个独立的相同流量源建模为点过程，将其送入速度与n成正比的链接中。在对输入过程的相当一般的假设下，我们表明缓冲区内容超过阈值b>0的稳态概率倾向于假设泊松输入过程的相应概率。我们验证了一大类通常用于数据流量建模的远程依赖源的假设。我们的结果表明，通过叠加，可以在比以前的结果（考虑O(n)缓冲区大小）更小的缓冲区上实现显着的多路复用增益。此外，模拟表明，对于超出概率的实际值和适度利用，在叠加源数量的合理值上收敛到泊松极限。这对于高速网络来说尤其重要，因为高速内存的成本非常高。
A key criterion in the design of high-speed networks is the probability that the buffer content exceeds a given threshold. We consider n independent identical traffic sources modelled as point processes, which are fed into a link with speed proportional to n. Under fairly general assumptions on the input processes we show that the steady state probability of the buffer content exceeding a threshold b>0 tends to the corresponding probability assuming Poisson input processes. We verify the assumptions for a large class of long-range dependent sources commonly used to model data traffic. Our results show that with superposition, significant multiplexing gains can be achieved for even smaller buffers than suggested by previous results, which consider O(n) buffer size. Moreover, simulations show that for realistic values of the exceedance probability and moderate utilisations, convergence to the Poisson limit takes place at reasonable values of the number of sources superposed. This is particularly relevant for high-speed networks in which the cost of high-speed memory is significant.