  This paper studies the augmented truncation of discrete-time block-monotone
Markov chains under geometric drift conditions. We first present a bound for
the total variation distance between the stationary distributions of an
original Markov chain and its augmented truncation. We also obtain such error
bounds for more general cases where an original Markov chain itself may not be
block-monotone but is block-wise dominated by a block-monotone Markov chain.
Finally we discuss the application of our results to GI/G/1-type Markov chains.
