End-to-End Delay Performance Analysis of Industrial Internet of Things: A Stochastic Network Calculus Perspective

In a hybrid scenario of 5G and Industrial Internet of Things (IIoT), there is a lack of a theoretical tool to analyze probabilistic end-to-end (E2E) delay. In this article, we provide a comprehensive procedure, which is based on stochastic network calculus (SNC) with moment-generating functions (MGFs), for calculating the E2E delay violation probability for the target traffic in IIoT. The particularity of the scenario is that the E2E network is composed of two segments: 1) the industrial wireless link challenged by the complex fading channel and 2) the multinode wired network that supports common schedulers. An improved concatenation theorem is proposed to calculate the service capability of the E2E network, and a method based on Meijer G-functions is proposed to calculate the MGF for the service processes of various wireless fading channels. We investigate the impacts of various resource allocation strategies (on both wireless and wired networks) and parameters (e.g., bandwidth, weight, and cycle time) on probabilistic E2E delay and provide numerical performance bounds. We show that the capability joint adaptation of the wireless and wired networks is the key to E2E service guarantee. Moreover, related parameters such as the weights and message sizes should be carefully considered to improve E2E delay.