  In Braverman et al. (2024), the authors prove that the stationary
distribution of a multiclass queueing network converges to the stationary
distribution of a semimartingale reflecting Brownian motion (SRBM) in heavy
traffic. Among the sufficient conditions for the convergence is that the
reflection matrix $R$ of the SRBM is "tight". In this paper, we study how we
can verify this tightness of $R$. For a $2$-dimensional SRBM, we give necessary
and sufficient conditions for $R$ to be tight, while, for a general dimension,
we only give sufficient conditions. We then apply these results to the SRBMs
arising from the diffusion approximations of multiclass queueing networks with
static buffer priority service disciplines that are studied in Braverman et al.
(2024). It is shown that $R$ is always tight for this network with two stations
if $R$ is defined and completely-S. For the case of more than two stations, it
is shown that $R$ is tight for reentrant lines with last-buffer-first-service
(LBFS) discipline, but it is not always tight for reentrant line with
first-buffer-first-service (FBFS) discipline.
