  Recently, due to the staggering growth of wireless data traffic,
heterogeneous networks have drawn tremendous attention due to the capabilities
of enhancing the capacity/coverage and to save energy consumption for the next
generation wireless networks. In this paper, we study a long-run user-centric
network selection problem in the 5G heterogeneous network, where the network
selection strategies of the users can be investigated dynamically. Unlike the
conventional studies on the long-run model, we incorporate the memory effect
and consider the fact that the decision-making of the users is affected by
their memory, i.e., their past service experience. Namely, the users select the
network based on not only their instantaneous achievable service experience but
also their past service experience within their memory. Specifically, we model
and study the interaction among the users in the framework of fractional
evolutionary game based on the classical evolutionary game theory and the
concept of the power-law memory. We analytically prove that the equilibrium of
the fractional evolutionary game exists, is unique and uniformly stable. We
also numerically demonstrate the stability of the fractional evolutionary
equilibrium. Extensive numerical results have been conducted to evaluate the
performance of the fractional evolutionary game. The numerical results have
revealed some insightful findings. For example, the user in the fractional
evolutionary game with positive memory effect can achieve a higher cumulative
utility compared with the user in the fractional evolutionary game with
negative memory effect. Moreover, the fractional evolutionary game with
positive memory effect can reduce the loss in the user's cumulative utility
caused by the small-scale fading.
