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In this paper, we consider a large-scale heterogeneous mobile edge computing system, where each device’s mean computing task arrival rate, mean service rate, mean energy consumption, and mean offloading latency are drawn from different bounded continuous probability distributions to reflect the diverse compute-intensive applications, mobile devices with different computing capabilities and battery efficiencies, and different types of wireless access networks (e.g., 4G/5G cellular networks, WiFi). We consider a class of distributed threshold-based randomized offloading policies and develop a threshold update algorithm based on its computational load, average offloading latency, average energy consumption, and edge server processing time, depending on the server utilization. We show that there always exists a unique Mean-Field Nash Equilibrium (MFNE) in the large-system limit when the task processing times of mobile devices follow an exponential distribution. This is achieved by carefully partitioning the space of mean arrival rates to account for the discrete structure of each device’s optimal threshold. Moreover, we show that our proposed threshold update algorithm converges to the MFNE. Finally, we perform simulations to corroborate our theoretical results and demonstrate that our proposed algorithm still performs well in more general setups based on the collected real-world data and outperforms the well-known probabilistic offloading policy. 

We study adaptive video streaming for multiple users in wireless access edge networks with unreliable channels. The key challenge is to jointly optimize the video bitrate adaptation and resource allocation such that the users' cumulative quality of experience is maximized. This problem is a finite-horizon restless multi-armed multi-action bandit problem and is provably hard to solve. To overcome this challenge, we propose a computationally appealing index policy entitled Quality Index Policy, which is well-defined without the Whittle indexability condition and is provably asymptotically optimal without the global attractor condition. These two conditions are widely needed in the design of most existing index policies, which are difficult to establish in general. Since the wireless access edge network environment is highly dynamic with system parameters unknown and time-varying, we further develop an index-aware reinforcement learning (RL) algorithm dubbed QA-UCB. We show that QA-UCB achieves a sub-linear regret with a low-complexity since it fully exploits the structure of the Quality Index Policy for making decisions. Extensive simulations using real-world traces demonstrate significant gains of proposed policies over conventional approaches. We note that the proposed framework for designing index policy and index-aware RL algorithm is of independent interest and could be useful for other large-scale multi-user problems.