Reduced-State, Optimal Scheduling for Decentralized Medium Access Control of a Class of Wireless Networks

Motivated by medium access control for resource-challenged wireless Internet of Things (IoT) networks, we consider the problem of queue scheduling with reduced queue state information. In particular, we consider a time-slotted scheduling model with $N$ wireless links, such that links $i$ and $i+1$ , $1 \leq i \leq N-1$ cannot transmit together. Our aim in this paper is to study throughput-optimal, and even delay optimal, scheduling policies that require only the empty-nonempty state of the packet queues associated with these links (Queue Nonemptiness Based, or QNB, policies). We focus on Maximum Size Matching (MSM) policies, and provide an analysis of all the QNB-MSM policies for $N=3$ , thereby comparing their performance, and revisiting a delay optimal scheduling result. Our study shows that, while scheduling a maximum size matching would seem intuitive, there are important performance differences between different QNB-MSM policies. Further, it is not necessary for a QNB policy to be MSM for it to be throughput optimal. We develop a new Policy Splicing technique to combine scheduling policies for small networks to construct throughput-optimal policies for larger networks, some of which also aim for low delay. For $N=3$ there exists a QNB-MSM policy that is sum-queue optimal over the entire stability region. We show, however, that for $N \geq 4$ , there is no QNB scheduling policy that is sum-queue length optimal over all arrival rate vectors in the capacity region. Our throughput-optimality results rely on two new arguments: a Lyapunov drift lemma specially adapted to policies that are queue length-agnostic, and a priority queueing analysis for showing strong stability. We then extend our results to a more general class of interference constraints that we call cluster-of-cliques (CoC) conflict graphs. We consider two types of CoC networks, namely, Linear Arrays of Cliques (LAoC) and Star-of-Cliques (SoC) networks. We develop QNB policies for these classes of networks, study their stability and delay properties, and propose and analyze techniques to reduce the amount of state information to be disseminated across the network for scheduling.