I-CSMA: A Link Scheduling Algorithm for Wireless Networks based on Ising Model

We propose a new randomized link scheduling algorithm for wireless networks, called I-CSMA, which is based on a modified version of the Ising model in physics. The main result is that I-CSMA is shown to be throughput-optimal. ICSMA is a generalization of earlier Glauber-dynamics-based, throughput-optimal algorithms such as Q-CSMA in that each earlier algorithm involves a truncated Markov chain of the Markov chain in I-CSMA. The main result implies that there is no need to truncate the Markov chain in the classical way by prohibiting transitions into the subset of the excluded states, which in this case are the link configurations with interference. The Markov chain can freely move over the entire space of link configurations. Other methods of “truncation” for producing a valid schedule work equally well in terms of achieving throughput-optimality. Therefore, the main result justifies the removal of a major restriction in earlier related algorithms, and allows the exploration and exploitation of that new freedom. Our simulation experiments show that I-CSMA leads to smaller queue sizes, and therefore, gives better delay performance. The I-CSMA algorithm is still decentralized and easily implementable. We also propose a heuristic I-CSMA algorithm, which is even simpler and yet has comparable performance to I-CSMA.