We consider the problem of maximizing utility in wireless backhaul networks, where utility is a function of satisfied service level agreements (SLAs), defined in terms of end-to-end packet delays and instantaneous throughput. We model backhaul networks as a tree topology and show that SLAs can be satisfied by constructing link schedules with bounded inter-scheduling times, an NP-complete problem known as pinwheel scheduling. For symmetric tree topologies, we show that simple round-robin schedules can be optimal under certain conditions. In the general case, we develop a mixed-integer program that optimizes over the set of admission decisions and pinwheel schedules. We develop a novel pinwheel scheduling algorithm, which significantly expands the set of schedules that can be found in polynomial time over the state of the art. Using conditions from this algorithm, we develop a scalable, distributed approach to solve the utility-maximization problem, with complexity that is linear in the depth of the tree.

翻译：本文研究无线回程网络中的效用最大化问题，其中效用是满足服务等级协议（SLA）的函数，该协议通过端到端数据包延迟和瞬时吞吐量来定义。我们将回程网络建模为树形拓扑结构，并证明通过构建具有有界调度间隔的链路调度方案可以满足SLA要求，该问题等价于NP完全的风车调度问题。对于对称树形拓扑，我们证明在特定条件下简单的轮询调度方案可以达到最优。在一般情形下，我们建立了混合整数规划模型，该模型在准入决策集合和风车调度方案集合上进行联合优化。我们提出了一种创新的风车调度算法，该算法在多项式时间内可求解的调度方案集合较现有技术实现了显著扩展。基于该算法的约束条件，我们开发了可扩展的分布式方法来解决效用最大化问题，其计算复杂度与树形结构的深度呈线性关系。