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FRASA: Feedback Retransmission Approximation for the Stability Region of Finite-User Slotted ALOHA

机译:FRASA:有限用户时隙ALOHA的稳定区域的反馈重传近似

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摘要

Feedback Retransmission Approximation for Slotted ALOHA (FRASA) is proposed to study the stability region of finite-user slotted ALOHA under the collision channel. With FRASA, the stability region is derived in closed form for any number of users in the system. The result derived from FRASA is shown to be identical to the analytical result of finite-user slotted ALOHA when there are two users. It is shown that the stability region obtained from FRASA is a good approximation to the stability region of finite-user slotted ALOHA. The convex hull bound, which is convex, piecewise linear and outer bounds the stability region of FRASA, is provided. $p$-convexity, an essential property that the stability region of FRASA should have to ensure the convex hull bound is close to the boundary, is characterized. From these, it is derived that the stability region of FRASA can never be convex when there are more than two users. A separate convex and piecewise linear inner bound on the stability region of FRASA, the supporting hyperplane bound, is also given.
机译:为了研究有限用户时隙ALOHA在冲突信道下的稳定区域,提出了时隙ALOHA的反馈重传近似方法。使用FRASA,系统中任何数量的用户都可以封闭形式导出稳定区域。当有两个用户时,从FRASA得出的结果与有限用户带时隙ALOHA的分析结果相同。结果表明,从FRASA获得的稳定性区域与有限用户开槽ALOHA的稳定性区域非常接近。提供了凸包边界,它是凸的,分段线性的并且是FRASA稳定区域的外部边界。表征了$ p $-凸性,FRASA的稳定区域必须具有此特性以确保凸包边界接近边界。从这些推论得出,当有两个以上的用户时,FRASA的稳定区域永远不会凸出。还给出了在FRASA稳定区域上的单独的凸和分段线性内边界,即支撑超平面边界。

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