One open problem is to show that, in a
discrete-time Markov chain with 'local' transitions, under suitable conditions, rapid mixing occurs essentially if and only if there is normal concentration of measure long-term and in equilibrium (with non-trivial bounds).
3 shows the proposed
discrete-time Markov chain model of the IEEE 802.15.6 MAC protocol in the unsaturated condition.
It is easy to model the process {i(t), s(t), b(t)} with
discrete-time Markov chain in the assumption that [p.sub.i] (collision probability) and [d.sub.n] (the channel busy probability during its backoff stage) are independent.
In [2], based on the assumption that collision probability is independent from the transmission history, a two-dimensional
discrete-time Markov chain model represented as a stochastic process (s(t),b(t)) is defined, where s(t) is the backoff stage i (0,1,...,m)at time t and b(t) is the backoff counter value k (0,1,..., [W.sup.i] - 1)at time t.
It supports analysis of several types of probabilistic models:
discrete-time Markov chains (DTMCs), continuous-time Markov chains (CTMCs), Markov decision processes (MDPs), probabilistic automata, and probabilistic timed automata.