We study a distributed user association algorithm for a heterogeneous wireless network with the objective of maximizing the sum of the utilities (on the received throughput of wireless users). We consider a state dependent wireless network, where the rate achieved by the users are a function of their user associations as well as the state of the system. We consider three different scenarios depending on the state evolution and the users$text{}$ knowledge of the system state. In this context, we present completely uncoupled user association algorithms for utility maximization where the users$text{}$ association is entirely a function of its past associations and its received throughput. In particular, the user is oblivious to the association of the other users in the network. Using the theory of perturbed Markov chains, we show the optimality of our algorithms under appropriate scenarios.
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