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Asymptotically Optimal Scheduling Schemes for Large Networks

Abstract : In this thesis, we investigate a general channel allocation problem where the number of channels is less than that of users. The aim is to find a policy that schedules the channels to a given subset of users at each time slot in such a way to minimize two different objectives functions namely, the long-run expected average queuing delay (chapter 3) and the long-run expected average age of information (Chapter 4). We show that our problems fall in the framework of Restless Bandit Problems (RBP), for which obtaining the optimal solution is known to be out of reach. To circumvent this difficulty, we tackle the problem by adopting a Whittle index approach. In Chapter 2, we explain the Lagrangian relaxation, the steady-state and discounted cost approaches used to obtain the expressions of Whittle indices. The structure of each subproblem’s optimal solution is provided in chapter 3 and 4 depending on the system models and the considered metrics (queue length or Age of Information). In Chapter 3, the objective of the scheduling problem is to minimize the total average backlog queues of the network in question. We apply the Lagrangian relaxation approach detailed in Chapter 2 for the present model, and we prove that the optimal solution of the one-dimensional problem is of type threshold policy. After that, we establish that the aforementioned problem is indexable. Armed with that, we apply the discounted cost approach when the queue size is infinite and the steady-state approach when the queue size is tight to obtain the Whittle indices expressions. We then provide rigorous mathematical proof that our policy is optimal in the infinitely many users regime. Finally, we provide numerical results that showcase the remarkable good performance of our proposed policy and that corroborate the theoretical findings. In Chapter 4, we examine the average age minimization problem where users transmit over unreliable channels. Similarly to the problem studied in Chapter 3, finding the optimal scheduling scheme is known to be challenging. Accordingly, we adopt the Whittle index approach to derive the Whittle indices. Our main contribution is to provide rigorous results on the asymptotic optimality of Whittle Index Policy (WIP) in the many-users regime when the state space of the age of information is finite. However, when the state space of the Age of Information is infinite, we provide a new mathematical approach to establish the optimality of WIP for specific network settings. This novel approach is based on intricate techniques, and unlike previous works in the literature, it is free of any mathematical assumptions. Finally, we lay out numerical results that corroborate our theoretical findings and demonstrate the policy’s notable performance in the many-users regime.
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Submitted on : Monday, May 31, 2021 - 4:16:08 PM
Last modification on : Tuesday, June 22, 2021 - 3:52:58 AM


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  • HAL Id : tel-03243493, version 1


Saad Kriouile. Asymptotically Optimal Scheduling Schemes for Large Networks. Networking and Internet Architecture [cs.NI]. Université Paris-Saclay, 2021. English. ⟨NNT : 2021UPASG022⟩. ⟨tel-03243493⟩



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