This paper discusses how latency guarantees for non-cyclic (feedforward) First-In-First-Out (FIFO) networks with shapers can be computed within the Network Calculus (NC) framework. Shapers are methods implemented in software or hardware and may reside inside the network and at the endpoint which constrain the rate and maximum packet sizes for the transmission of specific data streams (flows) or groups thereof. Shaping can improve latencies and is an important aspect of Time-Sensitive Networking (TSN). Several methods in NC exist to analyze FIFO networks. Among them is the Least Upper Delay Bound (LUDB) methodology. So far, LUDB does not incorporate shaping assumptions into its analysis. This paper addresses this gap resulting in the new methodology called LUDB++. The evaluation on a set of different line topologies and a tree topology with a total of 130 configurations shows that LUDB++ delivers more accurate latency bounds compared to LUDB. Moreover, the Exponential Linear Program (ELP) method, which considers FIFO and shaping inside the network, yields the most accurate bounds to this date. ELP is superseded by LUDB++ for most of cases by a margin of up to 9.13%.

翻译：本文探讨了如何在网络演算（NC）框架下计算带整形器的非循环（前馈）先入先出（FIFO）网络的延迟保证。整形器是以软件或硬件方式实现的方法，可驻留在网络内部或端点处，用于约束特定数据流（或流组）传输的速率和最大数据包大小。整形能够改善延迟，是时间敏感网络（TSN）的重要方面。网络演算中存在多种分析FIFO网络的方法，其中包括最小上界延迟（LUDB）方法。迄今为止，LUDB尚未将整形假设纳入其分析中。本文针对这一空白提出了名为LUDB++的新方法。对包含不同线形拓扑和一种树形拓扑在内的总计130种配置的评估表明，与LUDB相比，LUDB++能提供更精确的延迟界。此外，考虑网络内部FIFO与整形的指数线性规划（ELP）方法至今仍能给出最精确的界限。但在大部分情况下，LUDB++的精度已超越ELP，优势幅度最高可达9.13%。