  We examine the impact of torpid mixing and meta-stability issues on the delay
performance in wireless random-access networks. Focusing on regular meshes as
prototypical scenarios, we show that the mean delays in an $L\times L$ toric
grid with normalized load $\rho$ are of the order $(\frac{1}{1-\rho})^L$. This
superlinear delay scaling is to be contrasted with the usual linear growth of
the order $\frac{1}{1-\rho}$ in conventional queueing networks. The intuitive
explanation for the poor delay characteristics is that (i) high load requires a
high activity factor, (ii) a high activity factor implies extremely slow
transitions between dominant activity states, and (iii) slow transitions cause
starvation and hence excessively long queues and delays. Our proof method
combines both renewal and conductance arguments. A critical ingredient in
quantifying the long transition times is the derivation of the communication
height of the uniformized Markov chain associated with the activity process. We
also discuss connections with Glauber dynamics, conductance and mixing times.
Our proof framework can be applied to other topologies as well, and is also
relevant for the hard-core model in statistical physics and the sampling from
independent sets using single-site update Markov chains.
