  The goal of this paper is to identify exponential convergence rates and to
find computable bounds for them for Markov processes representing unreliable
Jackson networks. First we use the bounds of Lawler and Sokal in order to show
that, for unreliable Jackson networks, the spectral gap is strictly positive if
and only if the spectral gaps for the corresponding coordinate birth and death
processes are positive. Next, utilizing some results on birth and death
processes, we find bounds on the spectral gap for network processes in terms of
the hazard and equilibrium functions of the one dimensional marginal
distributions of the stationary distribution of the network. These
distributions must be in this case strongly light-tailed, in the sense that
their discrete hazard functions have to be separated from zero. We relate these
hazard functions with the corresponding networks' service rate functions using
the equilibrium rates of the stationary one dimensional marginal distributions.
We compare the obtained bounds on the spectral gap with some other known
bounds.
