Low-complexity scheduling algorithms with constant queue length and throughput guarantees

Distributed scheduling algorithms based on carrier sense multiple access (CSMA) are optimal in terms of the throughput and the steady-state queue lengths. However, they take a prohibitively long time to reach the steady-state, often exponential in the network size. Therefore for large networks that operate over a finite time horizon, apart from the guarantees on the steady-state queue lengths, performance guarantees on the short-term (i.e., transient) queuing behaviour are also required. To that end, we propose distributed scheduling algorithms that are guaranteed to have O(1) expected queue lengths not just in the steady-state but at every time instant, where O(⋅) is with respect to the network size. Further, our algorithms have O(1) complexity and support a constant fraction of the maximum throughput for typical wireless topologies. The central idea of our algorithms is to resolve collisions among pairs of conflicting nodes by assigning a master–follower hierarchy. The master–follower hierarchy can either be chosen randomly or based on the topology of the conflict graph, leading to different performance guarantees.