具有可变包的有限种群ALOHA的稳定性
Stability of Finite Population ALOHA with Variable Packets
摘要：
ALOHA是最基本的媒体访问控制（MAC）协议之一，并且代表了其他更复杂的分布式和异步MAC协议的基础，例如，CSMA。在本文中，不同于在传统的工作，侧重于平均值分析，我们研究了ALOHA信道上的分组传输延迟的分布特性。我们发现了一个新的现象，表明一个基本的有限人口ALOHA模型与可变大小（指数）的数据包的特点是幂律传输延迟，甚至可能导致零吞吐量。这些结果是在对比的经典工作，表现出指数延迟和积极的吞吐量有限人口ALOHA与固定的数据包。此外，我们描述了一个新的稳定性条件，这是完全来自尾部行为的数据包和回退分布，可能无法确定的平均值。幂律效应和可能的不稳定性可以通过减少数据包的可变性来减弱或消除。然而，我们发现，即使是时隙（同步）ALOHA与恒定大小的数据包可以表现出幂律延迟时，活跃用户的数量是随机的。从工程的角度来看，我们的研究结果意味着，数据包的大小和活跃用户的数量的变化需要考虑到设计强大的MAC协议时，特别是对于ad-hoc/传感器网络的其他因素，如链路故障和移动性，可能会进一步复杂的问题。
英文摘要：
ALOHA is one of the most basic Medium Access Control (MAC) protocols and represents a foundation for other more sophisticated distributed and asynchronous MAC protocols, e.g., CSMA. In this paper, unlike in the traditional work that focused on mean value analysis, we study the distributional properties of packet transmission delays over an ALOHA channel. We discover a new phenomenon showing that a basic finite population ALOHA model with variable size (exponential) packets is characterized by power law transmission delays, possibly even resulting in zero throughput. These results are in contrast to the classical work that shows exponential delays and positive throughput for finite population ALOHA with fixed packets. Furthermore, we characterize a new stability condition that is entirely derived from the tail behavior of the packet and backoff distributions that may not be determined by mean values. The power law effects and the possible instability might be diminished, or perhaps eliminated, by reducing the variability of packets. However, we show that even a slotted (synchronized) ALOHA with packets of constant size can exhibit power law delays when the number of active users is random. From an engineering perspective, our results imply that the variability of packet sizes and number of active users need to be taken into consideration when designing robust MAC protocols, especially for ad-hoc/sensor networks where other factors, such as link failures and mobility, might further compound the problem.
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