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 smart, and two 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 smart stream are routed to the shortest orbit queue, and in case of a tie, they choose an orbit randomly. Blocked jobs from the 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 modeling of wireless cooperative networks. We are interested in the asymptotic behavior 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 are agreed.

我们介绍了具有重试和两个无限容量轨道队列的广义连接最短队列模型。三个独立的泊松作业流，即一个智能作业流和两个专用作业流，流入一个单服务器系统，该系统最多可以容纳一个作业。发现服务器被占用的到达作业按如下方式路由到轨道：来自智能流的阻塞作业被路由到最短的轨道队列，如果出现平局，它们会随机选择一个轨道。来自专用的阻止作业流被直接路由到它们的轨道。轨道作业以不同的重试率重试连接服务器，即异构轨道队列。在无线协作网络的建模中发现了这种系统的应用。我们感兴趣的是该模型的平稳分布的渐近行为，前提是系统是稳定的。更准确地说，我们研究了最小轨道队列长度的尾部渐近线恰好是几何的条件。此外，我们应用启发式渐近方法来获得稳态联合轨道队列长度分布的近似值。提供了有用的数值示例，并表明通过渐近分析和启发式方法获得的结果是一致的。