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In this paper, we investigate uplink resource allocation for wireless local area network and cellular network interworking to provide multi-homing voice and data services. The problem is formulated based on the physical layer and medium access control layer technologies of the two networks to ensure that the resource allocation decisions are feasible and can be executed at the lower layers. Furthermore, to efficiently utilize users' equipment (UEs) battery power, the power distribution among multiple network interfaces of the UEs is included in the problem formulation. The optimal resource allocation problem is a multiple time-scale Markov decision process (MMDP) as the two networks operate at different time-scales and due to voice and data service requirements. We derive decision policies for the upper and the lower levels of the MMDP by decomposing each resource allocation problem over multiple time slots …