Delay bound analysis in real-time networks with priority scheduling using network calculus

Quality of Service (QoS) guarantees in large-scale real-time computing and communication networks are supported by enabling technologies such as real time scheduling, which can be implemented by priority scheduling. In order to guarantee the hard delay bound for delay sensitive applications, worst-case analysis has been developed. Network Calculus (NC) is a well known network analysis tool as it possesses a set of properties particularly suitable for large-scale networks. In NC, the arrival process and the service process of a system are bounded by the arrival curve and the service curve, respectively. These two curves are then used to derive the bounds of performance measures. However, due to the difficulty in properly choosing the curves, original NC based on min-plus algebra is not always able to provide tight performance bounds. In this paper, we develop a NC approach based on max-plus algebra and use it to derive the upper delay bound of a network system with non-preemptive priority scheduling. In max-plus NC, the arrival curve is defined as the lower bound on the cumulative inter-arrival time and the service curve gives the upper bound on the cumulative service time. Since we derive the worst-case cumulative service time for non-preemptive priority scheduling, these definitions allow us to choose the curves in such a way that they accurately capture the main characteristics of the arrivals and services. As a result, our max-plus NC approach generates tight delay bounds. In an example Controller Area Network (CAN) system, a series of numerical results for our delay bounds turn out to be as tight as the simulated worst-case delay. Therefore we prove that NC, as a suitable analytical method for large-scale real-time networks, is capable of providing accurate performance bounds.