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 $O\left(1\right)$ expected queue lengths not just in the steady-state but at every time instant, where $O\left(\cdot \right)$ is with respect to the network size. Further, our algorithms have $O\left(1\right)$ 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.

In addition to these hierarchical collision resolution algorithms, which are primarily designed for the conflict graph-based interference model, we also propose an Aloha-based algorithm for the $K$-neighbour collision tolerance interference model, which is a generalization of the conflict graph model. We show that the proposed Aloha-based algorithm supports a constant fraction of the maximum throughput for typical wireless topologies.