  By utilizing the combination of two powerful tools i.e., stochastic geometry
(SG) and evolutionary game theory (EGT), in this paper, we study the problem of
mobile user (MU) mode selection in heterogeneous sub-$6$ GHz/millimeter wave
(mmWave) cellular networks. Particularly, by using SG tools, we first propose
an analytical framework to assess the performance of the considered networks in
terms of average signal-to-interference-plus-noise (SINR) ratio, average rate,
and mobility-induced time overhead, for scenarios with user mobility{.}
According to the SG-based framework, an EGT-based approach is presented to
solve the problem of access mode selection. Specifically, two EGT-based models
are considered, where for each MU its utility function depends on the average
SINR and the average rate, respectively, while the time overhead is considered
as a penalty term. A distributed algorithm is proposed to reach the
evolutionary equilibrium, where the existence and stability of the equilibrium
is theoretically analyzed and proved. Moreover, we extend the formulation by
considering information delay exchange and evaluate its impact on the
convergence of the proposed algorithm. Our results reveal that the proposed
technique can offer better spectral efficiency and connectivity in
heterogeneous sub-$6$ GHz/mmWave cellular networks with mobility, compared with
the conventional access mode selection techniques.
