The aim of this work concerns the performance analysis of systems with interacting queues under the join the shortest queue policy. The case of two interacting queues results in a two-dimensional random walk with bounded transitions to non-neighboring states, which in turn results in complicated boundary behavior. Although this system violates the conditions of the compensation approach due to the transitions to non-neighboring states, we show how to extend the framework of the approach and how to apply it to the system at hand. Moreover, as an additional level of theoretic validation, we have compared the results obtained with the compensation approach with those obtained using the power series algorithm and we have shown that the compensation approach outperforms the power series algorithm in terms of numerical efficiency. In addition to the fundamental contribution, the results obtained are also of practical value, since our analysis constitutes a first attempt toward gaining insight into the performance of such interacting queues under the join the shortest queue policy. To fully comprehend the benefits of such a protocol, we compare its performance to the Bernoulli routing scheme as well as to that of the single relay system. Extensive numerical results show interesting insights into the system’s performance.

中文翻译：

---

具有冲突的协作随机接入网络中的最短中继队列策略分析

这项工作的目的涉及在加入最短队列策略下具有交互队列的系统的性能分析。两个交互队列的情况导致二维随机游走，有界转换到非相邻状态，进而导致复杂的边界行为。尽管该系统由于向非相邻状态的转换而违反了补偿方法的条件，但我们展示了如何扩展该方法的框架以及如何将其应用于手头的系统。此外，作为理论验证的附加级别，我们将补偿方法获得的结果与使用幂级数算法获得的结果进行了比较，我们已经证明补偿方法在数值效率方面优于幂级数算法。除了基本贡献之外，获得的结果也具有实用价值，因为我们的分析构成了在加入最短队列策略下深入了解此类交互队列性能的第一次尝试。为了充分理解这种协议的好处，我们将其性能与伯努利路由方案以及单中继系统的性能进行了比较。广泛的数值结果显示了对系统性能的有趣见解。我们将其性能与伯努利路由方案以及单中继系统的性能进行比较。广泛的数值结果显示了对系统性能的有趣见解。我们将其性能与伯努利路由方案以及单中继系统的性能进行比较。广泛的数值结果显示了对系统性能的有趣见解。