Efficient Exploration on Worst-Case Delay Performance of Networked Industrial Control Systems via Network Calculus and Deep Learning

As computer networking technologies such as Ethernet gain momentum in modern industrial control systems (ICSs), deterministic delay performance, which refers to the worst-case latencies provisioned by the network infrastructure, has become a critical property required by real-time control, automation, and operations. Although analytical methods that identify exact worst-case bounds on flow-specific communication delays have been proposed, there remain two hurdles discouraging further explorations of network-wide deterministic delay performance: (i) methods based on mixed integer linear programming (MILP) have high computational complexities; and (ii) existing methods are flow-specific. This paper proposes a deep-learning-assisted approach to understanding the deterministic delay performance of networked industrial control systems. Transforming flow-specific worst-case delay bounding into network-wide deterministic delay analysis, our approach facilitates the incorporation of application-specific hard-real-time performance constraints. By incorporating graph neural networks (GNNs), our approach significantly reduces the runtime costs and provides sufficiently tight approximations to the optimal MILP solutions. Through a combination of numerical analyses and simulations, we demon-strate that our approach enables the timely exploration of various worst-case scenarios, thereby paving the way for agile service provisioning in time-critical and/or delay-sensitive ICSs as well as model-based design of self-healing networked ICSs.

I. Introduction

Over the past few decades, the networked control sys-tem (NCS) paradigm [1]–[5], which is regarded as a class of networked cyber-physical systems (NCPSs), has become widely adopted by miscellaneous industrial control systems (ICSs), supporting time-critical and/or delay-sensitive applications ranging from power substation automation [6] to avionics control [7]. Switched Ethernet, due to its low costs, reliability, as well as ease of deployment and troubleshooting, has become one of the major networking technologies in modern ICSs, leading to specialized standards such as IEC 61850 [8], [9] and ARINC 664 [10], [11]. In contrast to dedicated hardwired connections in conventional ICSs with nearly-constant delays, switched Ethernet is shared among all the networked ICS devices and introduces various types of communication delays that must be carefully analyzed [1], [12], [13]. As the number and complexity of applications in modern ICSs grow, timely and accurately examining worst- case delay performance becomes vitally important for efficient network service provisioning as well as model-based self-healing ICS design under delay-constrained scenarios. Fig. 1.

Delay components of a single-switch Ethernet network, including propagation delays , transmission delays , processing delays and queueing delay .