  This paper studies a generic model for cooperative cognitive radio networks
where the secondary user is equipped with a finite relay queue as well as a
finite battery queue. Our prime objective is to characterize the stable
throughput region. Nevertheless, the complete characterization of the stable
throughput region for such system is notoriously difficult, since the
computation of the steady state distribution of the two-dimensional Markov
Chain (MC) model for both finite queues is prohibitively complex. We first
propose an algorithm to characterize the stable throughput region numerically,
and show its sheer computational complexity for large queue lengths. To lend
tractability and explore the nature of design parameters optimization at the
cognitive node, we next focus on two simpler systems, namely, finite battery
queue with infinite relay queue and finite relay queue with infinite battery
queue (referred henceforth as dominant system $1$ and $2$, respectively). For
each proposed dominant system, we investigate the maximum service rate of the
cognitive node subject to stability conditions. Despite the complexity of the
formulated optimization problems, due to their non-convexity, we exploit the
problems' structure to transform them into linear programs. Thus, we are able
to solve them efficiently using standard linear programming solvers. Our
numerical results demonstrate that, in practical systems, finite battery and
relay queues achieve the same level of benefits of a system with infinite queue
sizes, when their sizes are sufficiently large. They also reveal that the
achievable stable throughput region significantly expands when the arrival rate
of the energy harvesting process increases.
