In this paper, we study a delay-aware admission control (AC) and beam allocation (BA) problem with the consideration of quality of experience (QoE) and dynamic variation of channel condition for centralized unit (CU) and distributed unit (DU) based functional split options (FSOs) in millimeter wave (mmWave) fronthaul downlink networks. The original optimization problem aims to maximize timeaverage QoE subject to delay and queue stability constraints. The intractability of the considered problem comes from the necessity to allocate resources across periods of time slots. After applying virtual queue transformation and Lyapunov optimization method, the targeting problem can be converted into two independent AC and BA sub-problems in each time slot. The converted problem involves actual and virtual queues, which causes conflicting tendency. With the design of a flexible Lyapunov function, the influences of actual and virtual queues are theoretically to be proved balanced. Moreover, the AC sub-problem can be solved by Karush-Kuhn-Tucker condition, whereas mmWave BA sub-problem is tackled by genetic algorithm and matching game for the CU-based and DU-based FSOs, respectively. Simulation results demonstrate the applicability of the proposed CU-/DU-based algorithms in terms of average data rate, admission control rate, queue length, and corresponding system delay under either uniform or dense deployment of DUs. Moreover, the proposed scheme achieves the lowest delay and highest QoE performances while sustaining the system stability compared with the state-of-theart mechanisms in open literatures.
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