The stability region of the finite-user slotted ALOHA protocol
The stability region of the finite-user slotted ALOHA protocol
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DOI：
10.1109/cdc.1989.70180
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发表时间：
1989-12
期刊：
影响因子：
--
通讯作者：
V. Anantharam
中科院分区：
文献类型：
--
作者：
V. Anantharam
考虑的是一个版本的离散时间时隙ALOHA协议操作的多个缓冲终端。稳定区域被定义为到达率λ =（λ/sub 1/，. . ., lambda /sub M/），其中存在传输概率向量，使得系统稳定。假设到达在时隙之间是独立的，并且在任何时隙中的到达的总数是几何分布的，其中这样的到达在节点i处的概率是λ/sub i// Sigma λ/sub k/，在所有k上，独立于其它。在此到达模型下，证明了协议稳定域的闭合性与无反馈时冲突信道的香农容量域相同。基本的概率观察是，平稳分布和某些条件分布来自它有界的增长函数有正相关。类似的技术可以用于研究其他的队列交互系统。目前尚不清楚结果是否取决于到达分布的选择。
Consideration is given to a version of the discrete-time slotted ALOHA protocol operating with finitely many buffered terminals. The stability region is defined to be the set of vectors of arrival rates lambda =( lambda /sub 1/, . . ., lambda /sub M/) for which there exists a vector of transmission probabilities such that the system is stable. It is assumed that arrivals are independent from slot to slot and that the total number or arrivals in any slot is geometrically distributed, with the probability that such an arrival is at node i being lambda /sub i// Sigma lambda /sub k/, over all k, independent of others. With this arrival model it is proved that the closure of the stability region of the protocol is the same as the Shannon capacity region of the collision channel without feedback. The basic probabilistic observation is that the stationary distribution and certain conditional distributions derived from it have positive correlations for bounded increasing functions. Similar techniques may be of use in studying other interacting system of queues. At present it is not clear if the result depends on the choice of arrival distribution.>