  This paper discusses the error estimation of the last-column-block-augmented
northwest-corner truncation (LC-block-augmented truncation, for short) of
block-structured Markov chains (BSMCs) in continuous time. We first derive
upper bounds for the absolute difference between the time-averaged functionals
of a BSMC and its LC-block-augmented truncation, under the assumption that the
BSMC satisfies the general $f$-modulated drift condition. We then establish
computable bounds for a special case where the BSMC is exponentially ergodic.
To derive such computable bounds for the general case, we propose a method that
reduces BSMCs to be exponentially ergodic. We also apply the obtained bounds to
level-dependent quasi-birth-and-death processes (LD-QBDs), and discuss the
properties of the bounds through the numerical results on an M/M/$s$ retrial
queue, which is a representative example of LD-QBDs. Finally, we present
computable perturbation bounds for the stationary distribution vectors of
BSMCs.
