This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of M$\mid$M$\mid$1 queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of parallel G$\mid$G$\mid$1 queues. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.

翻译：本文针对一类通用并行系统的信息龄给出了尾界估计，并探讨了其潜在应用价值。并行系统出现在多频段移动网络、多技术无线接入或多路径协议等相关场景中。通常，对各通信信道的控制有限，随机的服务中断和拥塞会导致缓冲，从而损害信息龄。独立信道的并行使用有望改善这一状况，因为一个信道上的中断可由另一信道补偿。令人意外的是，对于著名的M$\mid$M$\mid$1队列，我们发现相反的情况：将容量集中在一个信道上比具有相同总容量的并行系统性能更优。由于目前缺乏其他类型并行队列的解决方案，无法进行推广。本文通过极小加代数证明了信息龄的对偶表示，该表示与有效带宽/容量理论及随机网络演算中的队列模型相关联。利用这些方法，我们推导了并行G$\mid$G$\mid$1队列信息龄的尾界。除了经典并行队列，我们还研究了马尔可夫信道，其中取决于信道的记忆性，我们展示了并行系统的真正优势。我们继续探究这一新发现，并深入分析何时应将容量集中在一个信道上，以及何时独立并行信道性能更优。通过仿真结果补充分析，我们评估了不同的更新策略、调度策略以及异构信道的使用——这对最新的多频段网络至关重要。