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We study a model of wireless networks where users move at speed s, which hasthe original feature of being defined through a fixed-point equation. Namely,we start from a two-class Processor-Sharing queue to model one representativecell of this network: class 1 users are not impatient (non-moving) and class 2users are impatient (moving). This model has five parameters, and we study thecase where one of these parameters is set as a function of the other fourthrough a fixed-point equation. This fixed-point equation captures the factthat the considered cell is in balance with the rest of the network. Thismodeling approach allows us to alleviate some drawbacks of earlier models ofmobile networks.  Our main and surprising finding is that for this model, mobility drasticallyimproves the heavy traffic behavior, going from the usual 1/(1-rho) scalingwithout mobility (i.e., when s=0) to a logarithmic scaling -log(1-rho) as soonas s>0. In the high load regime, this confirms that the performance of mobilesystem takes benefit from the spatial mobility of users. Other model extensionsand complementary methodological approaches to this heavy traffic analysis arefinally discussed.

Mobility can drastically improve the heavy traffic performance from 1/(1-rho) to -log(1-rho)