Mobility can drastically improve the heavy traffic performance from \(\frac{1}{1-\varrho }\) to \(\log (1/(1-\varrho ))\)

We study a model of wireless networks where users move at speed \(\theta \ge 0\), 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 \(\frac{1}{1-\varrho }\) scaling without mobility (i.e., when \(\theta = 0\)) to a logarithmic scaling \(\log (1/(1-\varrho ))\) as soon as \(\theta > 0\). 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.