Scheduling periodic messages on a shared link

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 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 classical scheduling and packing problems, but the periodicity introduces a new twist. We study how the problem behaves with regard to the load of the shared link. The main contributions are polynomial-time algorithms which 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.