Evaluation and improvement of response time bounds for real-time applications under non-pre-emptive Fixed Priority Scheduling

Real-time applications must be guaranteed with a bounded response time. The two main approaches for computing the upper bounds are worst-case schedulability analysis and Network Calculus, both of which are based on the analysis of a deterministic majoring trajectory. The first approach is issued from the results of Liu and Layland and gives what is called the worst-case response time for a given set of periodic tasks scheduled with fixed priority. The second approach, proposed by Cruz, gives an upper bound on delay for a set of (σ,ρ)-bounded message flows. Both approaches could be used to evaluate the end-to-end delay bound in the industrial switched Ethernet (the target application) in which the main traffic is periodic with or without jitters. However, the use of either the worst-case trajectory or (σ,ρ) trajectory produces overestimated delay bounds. Therefore, to minimize this overestimation, the paper proposes a comparative study of the delay bounds evaluated by both approaches for periodic (with or without jitters) arrival processes under Fixed Priority Scheduling. For this purpose, a relationship is given between jitter and the maximum burst size for an optimal transposition from the classical task model to the (σ,ρ)-constrained model. The paper also proposes a hybrid method to reduce the upper bound given Network Calculus for a multihop network. Numerical studies show the advantage of the method for reducing the estimation of the buffering requirement in each network element.