Cloud-RAN is a recent architecture for mobile networks where the processing units are located in distant data centers while, until now, they were attached to antennas. The main challenge, to fulfill protocol constraints, is to guarantee low latency for the periodic messages sent from each antenna to its processing unit and back. The problem we address is to find a periodic sending scheme of these messages \emph{without contention nor buffering}, when all messages are of the same size and the period is fixed. We study the periodic message assignment problem modeling this situation on a common topology, where contention arises from a single link shared by all antennas. The problem is reminiscent of coupled-task scheduling, but the periodicity introduces a new twist. We study how the problem behaves with regard to the \emph{load} of the shared link. The main contributions are polynomial-time algorithms which \emph{always} find a solution for an arbitrary size of messages and load at most $2/5$ or for messages of size one and load at most $\phi - 1$, the golden ratio conjugate. We also prove that a randomized greedy algorithm finds a solution on almost all instances with high probability, explaining why most greedy algorithms work so well in practice.

翻译：云无线接入网（Cloud-RAN）是移动网络的一种新型架构，其处理单元位于远端数据中心，而传统架构中处理单元附着于天线。为满足协议约束，主要挑战在于确保从每根天线到处理单元往返传输的周期性消息维持低延迟。本文研究的问题是：当所有消息具有相同大小且周期固定时，如何设计一种无竞争、无缓冲的周期性发送方案。我们在典型拓扑结构上对此周期性消息分配问题建模，其中竞争源于所有天线共享单一链路。该问题与耦合任务调度问题相似，但周期性引入全新特性。我们探究该问题如何随共享链路负载变化：主要贡献包括多项式时间算法，该算法在消息大小任意且负载不超过2/5时，或在消息大小为1且负载不超过黄金分割共轭值φ-1时，始终能给出可行解。我们还证明随机贪心算法能以高概率在几乎所有实例中找到可行解，这解释了为何多数贪心算法在实践中表现优异。