Network Calculus Approach for Packet Delay Variation Analysis of Multi-Hop Wired Networks

The Industrial Internet of Things (IIoT) has revolutionized businesses by changing the way data are used to make products and services more efficient, reliable, and profitable. To achieve the improvement goals, the IIoT must guarantee the real-time performance of industrial applications such as motion control, by providing stringent quality of service (QoS) assurances for their (industrial applications) communication networks. An application or service may malfunction without adequate network QoS, resulting in potential product failures. Since an acceptable end-to-end delay and low jitter or packet delay variation (PDV) are closely related to quality of service (QoS), their impact is significant in ensuring the real-time performance of industrial applications. Although a communication network topology ensures certain jitter levels, its real-life performance is affected by dynamic traffic due to the changing number of devices, services, and applications present in the communication network. Hence, it is essential to study the jitter experienced by real-time traffic in the presence of background traffic and how it can be maintained within the limits to ensure a certain level of QoS. This paper presents a probabilistic network calculus approach that uses moment-generating functions to analyze the delay and PDV incurred by the traffic flows of interest in a wired packet switched multi-stage network. The presented work derives closed-form, end-to-end, probabilistic performance bounds for delay and PDV for several servers in series in the presence of background traffic. The PDV analysis conducted with the help of a Markovian traffic model for background traffic showed that the parameters from the background traffic significantly impact PDV and that PDV can be maintained under the limits by controlling the shape of the background traffic. For the studied configurations, the model parameters can change the PDV bound from 1 ms to 100 ms. The results indicated the possibility of using the model parameters as a shaper of the background traffic. Thus, the analysis can be beneficial in providing QoS assurances for real-time applications.