Abstract We study a model of wireless networks where users move at speed $$\theta \ge 0$$θ≥0, which has the original feature of being defined through a fixed-point equation. Namely, we start from a two-class processor-sharing queue to model one representative cell of this network: class 1 users are patient (non-moving) and class 2 users are impatient (moving). This model has five parameters, and we study the case where one of these parameters is set as a function of the other four through a fixed-point equation. This fixed-point equation captures the fact that the considered cell is in balance with the rest of the network. This modeling approach allows us to alleviate some drawbacks of earlier models of mobile networks. Our main and surprising finding is that for this model, mobility drastically improves the heavy traffic behavior, going from the usual $$\frac{1}{1-\varrho }$$11-ϱ scaling without mobility (i.e., when $$\theta = 0$$θ=0) to a logarithmic scaling $$\log (1/(1-\varrho ))$$log(1/(1-ϱ)) as soon as $$\theta > 0$$θ>0. In the high load regime, this confirms that the performance of mobile systems benefits from the spatial mobility of users. Finally, other model extensions and complementary methodological approaches to this heavy traffic analysis are discussed.

中文翻译：

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移动性可以极大地提高大流量性能，从 $$\frac{1}{1-\varrho }$$11-ϱ 到 $$\log (1/(1-\varrho ))$$log(1/(1- ⅱ))

摘要 我们研究了一个无线网络模型，其中用户以$$\theta \ge 0$$θ≥0 的速度移动，该模型具有通过定点方程定义的原始特征。即，我们从两类处理器共享队列开始，对该网络的一个代表性单元进行建模：类 1 用户耐心（不动），类 2 用户不耐烦（移动）。该模型有五个参数，我们研究了通过定点方程将其中一个参数设置为其他四个参数的函数的情况。这个定点方程捕获了这样一个事实，即所考虑的单元与网络的其余部分保持平衡。这种建模方法使我们能够减轻早期移动网络模型的一些缺点。我们主要和令人惊讶的发现是，对于这个模型，移动性极大地改善了交通繁忙的行为，从通常的 $$\frac{1}{1-\varrho }$$11-ϱ 没有移动性的缩放（即，当 $$\theta = 0$$θ=0 时）到对数缩放 $$\log (1 /(1-\varrho ))$$log(1/(1-ϱ)) 只要 $$\theta > 0$$θ>0。在高负载情况下，这证实了移动系统的性能受益于用户的空间移动性。最后，讨论了这种大流量分析的其他模型扩展和补充方法论方法。