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A key element to realizing the smart energy grid of the future is the deployment of an efficient and reliable information network. An intelligent combination of wired networks (the Internet), wireless networks and power line communication networks can be used to deliver control and application messages generated by the smart grid. Integration of these three network types is non-trivial due to the distinct differences in deliverable quality of service and financial cost. Traffic assignment across these distinct networks poses a novel research problem which must be solved to realize the smart grid. Herein, an algorithm which dynamically allocates traffic with different Quality of Service requirements in terms of throughput, delay and failure probability to information networks with different performance characteristics is proposed. A detailed queueing model for the system is defined which accounts for input queues buffering smart grid packets and external applications injecting traffic into the buffers of the networks. A Lyapunov optimization based- algorithm selects the packet allocation strategy based on input/output queue states and guarantees the required QoS to the input queues while minimizing financial cost.