A high-order Markov chain based scheduling algorithm for low delay in CSMA networks

Recently, several CSMA algorithms based on the Glauber dynamics model have been proposed for multihop wireless scheduling, as viable solutions to achieve the throughput optimality, yet simple to implement. However, their delay performance still remains unsatisfactory, mainly due to the nature of the underlying Markov chains that imposes a fundamental constraint on how the link state can evolve over time. In this paper, we propose a new approach toward better queueing delay performance, based on our observation that the algorithm needs not be Markovian, as long as it can be implemented in a distributed manner. Our approach hinges upon utilizing past state information observed by local link and then constructing a high-order Markov chain for the evolution of the feasible link schedules. We show in theory and simulation that our proposed algorithm, named delayed CSMA, achieves the throughput optimality, and also provides much better delay performance by effectively `de-correlating´ the link state process (and thus resolves link starvation). Our extensive simulations demonstrate that the delay under our algorithm can be often reduced by a factor of 20 over a wide range of scenarios, compared to the standard Glauber-dynamics-based CSMA algorithm.