In this article, we investigate the transient behavior of a sequence of packets/bits traversing a multi-hop wireless network under static routing. Our work is motivated by novel applications from the domain of process automation, Machine-Type Communication (MTC) and cyber-physical systems, where short messages are communicated and statistical guarantees need to be provided on a per-message level. In order to optimize such a network, apart from understanding the stationary system dynamics, an understanding of the short-term dynamics (i.e. transient behavior) is also required. To this end, we derive novel Wireless Transient Bounds (WTB) for end-to-end delay and backlog in a multi-hop wireless network using stochastic network calculus approach. We start by analyzing a single end-to-end path, i.e. a line topology, and then we show how the obtained results can be applied to a mesh network with static routing using a concept called ’ leftover service ’. WTB depends on the initial backlog at each node as well as the instantaneous channel states. We numerically compare WTB with Kernel-Based-Transient Bound (KBTB), which can be obtained by adapting existing stationary bound, as well as simulated end-to-end delay of the investigated network. While KBTB and stationary bounds are not able to capture the short-term system dynamics well, WTB provides relatively tight upper bound and has a decay rate that closely matches the simulation. This is achieved by WTB only with a slight increase in the computational complexity, by a factor of $O(T+N)$ , where $T$ is the duration of the arriving sequence and $N$ is the number of hops in the network. We believe that the presented analysis and the bounds are necessary tools for future work on transient network optimization for many important emerging applications, e.g., massive MTC, critical MTC, edge computing and autonomous vehicle.

中文翻译：

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静态路由下多跳无线网络的瞬态分析

在本文中，我们研究了在静态路由下遍历多跳无线网络的一系列数据包/位的瞬时行为。我们的工作是由过程自动化，机器类型通信（MTC）和网络物理系统领域中的新颖应用程序激发的，在这些领域中，要传达短消息并需要在每个消息级别提供统计保证。为了优化这样的网络，除了了解固定系统动力学之外，还需要了解短期动力学（即瞬态行为）。为此，我们使用随机网络演算方法推导了用于多跳无线网络中端到端延迟和积压的新颖无线瞬态边界（WTB）。我们首先分析一条端到端的路径，即线形拓扑，剩余服务 '。WTB取决于每个节点上的初始积压以及瞬时通道状态。我们将WTB与基于内核的临时边界（KBTB）进行了数值比较，可以通过调整现有的固定边界以及所研究网络的模拟端到端延迟来获得。虽然KBTB和固定范围无法很好地捕获短期系统动态，但WTB提供了相对严格的上限，并且衰减速率与模拟非常匹配。这是通过WTB实现的，只是计算复杂性略有增加，增加了 $ O（T + N）$ ，在哪里 $ T $ 是到达序列的持续时间， $ N $ 是网络中的跃点数。我们认为，对于大量重要的新兴应用，例如大规模MTC，关键MTC，边缘计算和自动驾驶汽车，目前的分析和界限是进行瞬态网络优化的未来工作的必要工具。