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Efficient distributed resource allocation and users to cells assignment over a heterogeneous integrated wireless environment is addressed, where multiple-access technologies coexist and cooperate toward achieving network-wide quality-of-service (QoS)-aware utility-based performance optimization. The integrated network is viewed as a global optimizer under appropriate intracell resource allocation constraints. Multiaccess diversity is addressed by setting a user-centric service-aware goal, thus maximizing users' QoS-aware service performance satisfaction, as expressed through properly assigned utility functions. The integrated network utility maximization problem is treated through a two-level dual-decomposition methodology, leading to a low-complexity distributed iterative subgradient algorithm for attaining a network-wide near-optimal operation point. Extensive numerical results verify the analytical claims, demonstrate the applicability of the proposed framework, and illustrate that significant performance gains can be achieved over popular existing resource allocation schemes.