  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 are simple to implement. However, their delay
performances still remain 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 and delay performance, based on our observation that the
algorithm needs not be Markovian, as long as it can be implemented in a
distributed manner, achieve the same throughput optimality, while offering far
better delay performance for general network topologies. 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, adds virtually no additional overhead onto the existing
CSMA-based algorithms, achieves the throughput optimality under the usual
choice of link weight as a function of local queue length, and also provides
much better delay performance by effectively `de-correlating' the link state
process (thus removing link starvation) under any arbitrary network topology.
From our extensive simulations we observe 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.
