マルコフ連鎖、ルーターの確認

最近線形力学系を学びながらマルコフ連鎖を見ています。It seems that, given a probability distribution that a system is in any state (from a discrete set) and the transition matrix between states, the probability distribution after some number of time periods can be quickly computed. Say that the distribution for a 2 state system at t=0 is [.4 .6]=p(0). Assume also that the transition probabilities are
[.9 .8]
[.1 .2] = P
where column 1 is the probabilities of transition given that the system is in state 1.
Then the probability distribution at t=2 is given by:
P^2p(0).
シスコはルーターの状態を他の機器から確認するために複数なプロトコルがありそうです。　　SNMP, IP traffic export, netflow, IP SLA, RMON and embedded event manager all seem to provide similar functionality.