Centrum Voor Wiskunde En Informatica the Busy Period in the Fluid Queue
Centrum Voor Wiskunde En Informatica the Busy Period in the Fluid Queue
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Centrum Voor Wiskunde En Informatica 流动队列中的繁忙时期
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通讯作者：
V. Dumas Cwi
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作者：
O. Boxma;V. Dumas;V. Dumas Cwi
考虑一个由N /o个源提供的uid队列。假设源的消声周期呈指数分布，而源的活跃期呈一般分布。每个源的创新率，在活动时，至少与买方的流出率一样大。我们对该模型的性能分析做出了两项贡献。首先，我们确定了从源i的活跃周期开始的繁忙周期分布的Laplace-Stieltjes变换，i = 1；：：：；N，作为0的唯一解；1] N个方程中的N个。由此我们也得到了任意繁忙周期分布的Laplace-Stieltjes变换。其次，我们将繁忙期分布的尾部行为与活动期分布的尾部行为联系起来。我们表明，所有繁忙期分布的尾部都有规律地变化指数？(2)活动期尾尾最重的指数分布有规律变化。我们根据后者提供了前者的明确等价物，这表明具有较轻相关尾部的源的贡献相当于输出速率的简单降低。这些结果对uid队列网络的性能分析具有启示意义。
Consider a uid queue fed by N on/oo sources. It is assumed that the silence periods of the sources are exponentially distributed, whereas the activity periods are generally distributed. The innow rate of each source, when active, is at least as large as the outtow rate of the buuer. We make two contributions to the performance analysis of this model. Firstly, we determine the Laplace-Stieltjes transforms of the distributions of the busy periods that start with an active period of source i, i = 1; : : : ; N , as the unique solution in 0; 1] N of a set of N equations. Thus we also nd the Laplace-Stieltjes transform of the distribution of an arbitrary busy period. Secondly, we relate the tail behaviour of the busy period distributions to the tail behaviour of the activity period distributions. We show that the tails of all busy period distributions are regularly varying of index ? ii the heaviest of the tails of the activity period distributions are regularly varying of index ?. We provide explicit equivalents of the former in terms of the latter, which show that the contribution of the sources with lighter associated tails is equivalent to a simple reduction of the outtow rate. These results have implications for the performance analysis of networks of uid queues.