  We introduce the generalized join the shortest queue model with retrials and
two infinite capacity orbit queues. Three independent Poisson streams of jobs,
namely a \textit{smart}, and two \textit{dedicated} streams, flow into a single
server system, which can hold at most one job. Arriving jobs that find the
server occupied are routed to the orbits as follows: Blocked jobs from the
\textit{smart} stream are routed to the shortest orbit queue, and in case of a
tie, they choose an orbit randomly. Blocked jobs from the \textit{dedicated}
streams are routed directly to their orbits. Orbiting jobs retry to connect
with the server at different retrial rates, i.e., heterogeneous orbit queues.
Applications of such a system are found in the modelling of wireless
cooperative networks. We are interested in the asymptotic behaviour of the
stationary distribution of this model, provided that the system is stable. More
precisely, we investigate the conditions under which the tail asymptotic of the
minimum orbit queue length is exactly geometric. Moreover, we apply a heuristic
asymptotic approach to obtain approximations of the steady-state joint orbit
queue-length distribution. Useful numerical examples are presented and shown
that the results obtained through the asymptotic analysis and the heuristic
approach agreed.
