Cooperation in multi-access wireless networks have become an effective strategy for answering the rising data rate requests. The interworking is performed either by traffic steering, load balancing or yet radio resource aggregation, the so-called multi-homing. While most studies focused mainly on the first two techniques, we focus in this work on multi- homing, and target principally LTE and WiFi access networks. We specifically consider the co-existence of several classes of users in the system: single-homed users and multi- homed users, and study two network-centric, resource allocation strategies: proportional fairness applied to the global network as a whole or to each wireless access network in isolation of the other. We evaluate the system performance and show that both strategies improve the achievable throughput and stability conditions by applying a load balancing between accesses, thus increasing the overall network capacity