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Temporal starvation in multi-channel CSMA networks: an analytical framework

机译：多通道CSMA网络中的时间饥饿：一个分析框架

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摘要

In this paper we consider a stochastic model for a frequency-agile CSMA protocol for wireless networks where multiple orthogonal frequency channels are available. Even when the possible interference on the different channels is described by different conflict graphs, we show that the network dynamics can be equivalently described as that of a single-channel CSMA algorithm on an appropriate virtual network. Our focus is on the asymptotic regime in which the network nodes try to activate aggressively in order to achieve maximum throughput. Of particular interest is the scenario where the number of available channels is not sufficient for all nodes of the network to be simultaneously active and the well-studied temporal starvation issues of the single-channel CSMA dynamics persist. For most networks we expect that a larger number of available channels should alleviate these temporal starvation issues. However, we prove that the aggregate throughput is a non-increasing function of the number of available channels. To investigate this trade-off that emerges between aggregate throughput and temporal starvation phenomena, we propose an analytical framework to study the transient dynamics of multi-channel CSMA networks by means of first hitting times. Our analysis further reveals that the mixing time of the activity process does not always correctly characterize the temporal starvation in the multi-channel scenario and often leads to pessimistic performance estimates.
机译：在本文中，我们考虑了适用于无线网络的频率捷变CSMA协议的随机模型，其中有多个正交频率信道可用。即使通过不同的冲突图描述了不同信道上的可能干扰，我们也表明，网络动力学可以等效地描述为适当虚拟网络上的单信道CSMA算法。我们的重点是渐进机制，其中网络节点尝试积极激活以实现最大吞吐量。特别令人感兴趣的是以下情况：可用通道的数量不足以同时激活网络的所有节点，并且单通道CSMA动态的经过充分研究的时间匮乏问题仍然存在。对于大多数网络，我们希望有更多的可用信道可以缓解这些暂时的饥饿问题。但是，我们证明了总吞吐量是可用通道数的不增加函数。为了研究总吞吐量和时间饥饿现象之间出现的这种折衷，我们提出了一个分析框架，通过首次命中时间来研究多通道CSMA网络的瞬态动力学。我们的分析进一步揭示，活动过程的混合时间并不总是正确地表征多渠道情景中的时间饥饿，并且常常导致悲观的绩效估计。

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