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Large-scale Internet applications, such as content distribution networks, are deployed in a geographically distributed manner and emit massive amounts of carbon footprint at the data center. To provide uniform low access latencies, Cisco has introduced Fog computing as a new paradigm which can transform the network edge into a distributed computing infrastructure for applications. Fog nodes are geographically distributed and the deployment size at each location reflects the regional demand for the application. Thus, we need to control the fraction of user traffic to data center to maximize the social welfare. In this paper, we consider the emerging problem of joint resource allocation and minimizing carbon footprint problem for video streaming service in Fog computing. To solve the largescale optimization, we develop a distributed algorithm based on the proximal algorithm and alternating direction method of multipliers (ADMM). The numerical results show that our algorithm converges to near optimum within fifteen iterations, and is insensitive to step sizes.

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