A simple practical approximation is studied for a two-stage tandem que
ue with a finite first station. Explicit small error bounds are obtain
ed for the mean queue length and the tail probabilities of the second
queue. These error bounds are based on a new application of an existin
g error bound theorem for comparing Markov chains. The extension requi
res the so-called bias-terms to be bounded by a bounding function that
can be unbounded or oppositely become small. The extension is of inte
rest for further exploitation. (C) 1997 Elsevier Science B.V.