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.

翻译：我们引入了通用加入最短的队列模式, 包括重审和两个无限容量的轨道队列。 三个独立的 Poisson 工作流, 即 \ textit{ smart} 和 2\ textit{ dedited} 流, 流到一个服务器系统, 最多可以维持一个工作。 找到服务器占用的进站工作被选择到以下轨道: 从\ textit{ smart} 流到最短的轨道队列, 并且如果有一条线条, 它们随机选择一个轨道。 从\ textit{ dediated} 流到他们的轨道的阻塞工作直接被选择到他们的轨道。 运行工作重新连接到服务器, 以不同的重审速度, 即多轨道队列。 这种系统的应用在无线合作网络的建模中找到。 我们感兴趣的是这个模型的站位分布的无症状行为, 只要这个系统是稳定的。 更准确地说, 我们调查一个尾部作为最低轨道队列的尾部的定线串列路径是精确的几何测量的路径。 此外, 使用一个我们所展示的轨道阵列的模拟分析结果 。 。 使用一个持续的直观矩阵分布 以获得的轨距分析 。