Key points are not available for this paper at this time.
A natural and easily verifiable sufficient condition is given for the nonergodicity of a Markov chain. The result provides a converse to a theorem of Pakes and implies as special cases several recently published sufficient conditions for the instability of various forms of slotted ALOHA systems with Markovian retransmissions.
М. А. Каплан (Sun,) studied this question.