Binomial-Poisson entropic inequalities and the M/M/$\infty$ queue
Binomial-Poisson entropic inequalities and the M/M/$\infty$ queue
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二项式泊松熵不等式和 M/M/$infty$ 队列
DOI：
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发表时间：
2005
期刊：
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通讯作者：
Djalil CHAFAÏ
中科院分区：
文献类型：
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作者：
Djalil CHAFAÏ
本文给出了二项泊松分布的熵不等式。它们表现为M/M/$\infty$排队的局部不等式。他们特别描述了指数耗散的$\Phi$-熵沿着这个过程。这个简单的泊松过程表现为"常曲率“的模型，并且对于简单的泊松过程起着布朗运动的奥恩斯坦-乌伦贝克过程所起的作用。一些不等式通过半群插值得到了恢复。此外，我们探讨这些熵的不平等的行为下，一个特定的缩放，它认为奥恩斯坦-乌伦贝克过程作为一个流体限制的M/M/$\infty$队列。证明是基本的，并且基本上依赖于“$\Phi$-演算”的发展。
This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/$\infty$ queue. They describe in particular the exponential dissipation of $\Phi$-entropies along this process. This simple queueing process appears as a model of ``constant curvature'', and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semi-group interpolation. Additionally, we explore the behaviour of these entropic inequalities under a particular scaling, which sees the Ornstein-Uhlenbeck process as a fluid limit of M/M/$\infty$ queues. Proofs are elementary and rely essentially on the development of a ``$\Phi$-calculus''.