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We introduce the \textit{generalized join the shortest queue model withretrials} and two infinite capacity orbit queues. Three independent Poissonstreams 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 jobsthat find the server occupied are routed to the orbits as follows: Blocked jobsfrom the \textit{smart} stream are routed to the shortest orbit queue, and incase of a tie, they choose an orbit randomly. Blocked jobs from the\textit{dedicated} streams are routed directly to their orbits. Orbiting jobsretry to connect with the server at different retrial rates, i.e.,heterogeneous orbit queues. Applications of such a system are found in themodelling of wireless cooperative networks. We are interested in the asymptoticbehaviour of the stationary distribution of this model, provided that thesystem is stable. More precisely, we investigate the conditions under which thetail asymptotic of the minimum orbit queue length is exactly geometric.Moreover, we apply a heuristic asymptotic approach to obtain approximations ofthe steady-state joint orbit queue-length distribution. Useful numericalexamples are presented, and shown that the results obtained through theasymptotic analysis and the heuristic approach agreed.

The generalized join the shortest orbit queue system: Stability, exact tail asymptotics and stationary approximations