This article aims to investigate the performance of the IEEE 802.11-based tree-topology network, where a wireless node is within the others’ carrier sensing ranges. In such a network, the concurrent transmission is a dominant cause of frame collisions. Moreover, the relay nodes (RN) (i.e., in the tree) likely cause the coexistence of non-saturated and saturated nodes in the networks. Those conditions have not been addressed in the previous works yet. As a solution, this work proposes new analytical expressions of delay and throughput in the investigated scenario. The presented analytical model incorporates the Bianchi model and airtime concept to formulate operations of the IEEE 802.11 nodes. First, by leveraging Bianchi-based analysis, the proposed model gives the frame collision probability caused by concurrent transmission. Second, by using airtime concept analysis, the ratio of frame numbers of each flow in a relay node (RN) is expressed to represent the buffer state of RN. As a result, we can obtain the network throughput, the throughput, and the delay of each flow. The validity of the analytical expressions is confirmed by the quantitative agreement between the analytical and simulation results.

中文翻译：

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基于IEEE 802.11的树形拓扑网络的吞吐量和延迟分析

本文旨在研究基于IEEE 802.11的树形拓扑网络的性能，其中无线节点位于其他节点的载波侦听范围内。在这样的网络中，并发传输是帧冲突的主要原因。此外，中继节点（RN）（即，树中）可能导致网络中非饱和和饱和节点的共存。这些条件尚未在以前的工作中得到解决。作为解决方案，这项工作提出了在所研究场景中延迟和吞吐量的新分析表达式。提出的分析模型结合了Bianchi模型和广播时间概念来制定IEEE 802.11节点的操作。首先，通过利用基于Bianchi的分析，该模型给出了由并发传输引起的帧冲突概率。第二，通过广播时间概念分析，表示中继节点（RN）中每个流的帧数之比，以表示RN的缓冲区状态。结果，我们可以获得网络吞吐量，吞吐量和每个流的延迟。分析表达式与模拟结果之间的定量一致性证实了分析表达式的有效性。