  We analyze an interacting queueing network on $\mathbb{Z}^d$ that was
introduced in Sankararaman-Baccelli-Foss (2019) as a model for wireless
networks. We show that the marginals of the minimal stationary distribution
have exponential tails. This is used to furnish asymptotics for the maximum
steady state queue length in growing boxes around the origin. We also establish
a decay of correlations which shows that the minimal stationary distribution is
strongly mixing, and hence, ergodic with respect to translations on
$\mathbb{Z}^d$.
