Asymptotically optimal delay-aware scheduling in wireless networks
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In this paper, we investigate a channel allocation problem in networks taking into account the queues of users. Typically, there are less available channels than users, and at each slot the channels are allocated to users in such a way to minimize the total average queues in the network. We show that the problem falls in the framework of Restless Bandit Problems (RBP), for which obtaining the optimal solution is out of reach. This problem is analyzed in this paper using Whittle index approach. First, using the Lagrangian relaxation method, we provide a relaxed problem and show that it can be decomposed into simpler one-dimensional subproblems for which the optimal solution is a threshold-based policy. This allows us to characterize Whittle's indices for these one-dimensional systems and to develop an index-based heuristic policy for the original scheduling problem. We prove that this heuristic is asymptotically optimal in the infinitely many users regime and provide numerical results that illustrate its remarkably good performance.
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