## 1 Introduction  
The Industrial Internet of Things (IIoT) promises to achieve improved productivity, reliability, and revenues in the automation business by connecting embedded devices to \"the Internet\" [1]. As a global communication infrastructure, the Internet is anticipated to support real-time applications requiring a high level of quality of service (QoS). Industrial systems typically provide real-time and non-real-time services. Real-time services usually have strict QoS constraints not only on delay, but also, even stricter, on jitter or packet delay variation (PDV). PDV is the difference in the end-to-end one-way delay between selected packets in a flow with any lost packets being ignored. The IIoT must guarantee the real-time performance of industrial processes as a product may malfunction or fail in the absence of such assurances. The real-time performance of the IIoT is affected by many subsystems, such as sensor data capture, data processing, communication, production control, and operational activities. In motion control applications, a process is controlled by the message output that is generated from the process loop. Having a constant loop time is a crucial requirement for controlling the process in an efficient manner. Since jitter expresses the amount of deviation from the expected loop response time, in such applications, it is more critical than network speed. Most industrial Ethernet networks claim to have a low jitter. Its real-world performance, however, may differ depending on how much jitter exists in other network devices and how many cascaded devices the packets pass through. Another category of real-time applications utilizing the Internet in a commercial domain is multi-media applications, e.g., voice over IP (VoIP), streaming video, and online gaming. It is common for real-time voice or video applications to generate continuous traffic streams. For such traffic, jitter is an influential performance metric, which determines how much distortion occurs between a source and a destination through a packet stream in between them [2]. The distortion is as a result of multiple multiplexing operations between network routers and background traffic. It is possible to reduce real-time multi-media service disruptions such as clipped words, disruptions in service, and call drop-outs by maintaining a network jitter below an acceptable level. Thus, the current and future industrial communication networks involve a high data rate, best-effort traffic, working alongside real-time traffic for time-critical applications with hard deadlines. All time-critical applications require certain levels of QoS for smooth operation. QoS is expressed in terms of one-way delay, jitter, and packet loss. In many such applications, jitter has stricter restrictions to ensure QoS guarantees. Keeping jitter within certain limits is challenging in an ever-expanding communication network due to the growing number of devices, services, and applications. Hence, it is significant to explore the impact of non-real-time services on real-time services from a jitter perspective. In this paper, we study the end-to-end delay and PDV in a multi-hop wired packet switched network using a network-calculus-based approach and investigate the impact of the network parameters on PDV. The hypothesis of this work is that the PDV experienced by the traffic of interest can be amended by changing the shape of the background traffic. We carried out the analysis to test the validity of this hypothesis. The outcome of the analysis is beneficial in developing approaches for keeping network PDV below certain limits by controlling the network parameters. Traditionally, network calculus facilitates a worst-case analysis of networking queues and allows the derivation of deterministic performance bounds on delays. However, the worst-case scenarios rarely happen in practice. Thus, the deterministic performance bounds are pessimistic and often overestimate the network resources.