Programming and Verifying Real-Time Systems by Means of the Synchronous Data-Flow Language LUSTRE
IEEE Transactions on Software Engineering - Special issue: specification and analysis of real-time systems
Combining simulation and formal methods for system-level performance analysis
Proceedings of the conference on Design, automation and test in Europe: Proceedings
RTSS '07 Proceedings of the 28th IEEE International Real-Time Systems Symposium
An Algorithmic Toolbox for Network Calculus
Discrete Event Dynamic Systems
EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
ECRTS '10 Proceedings of the 2010 22nd Euromicro Conference on Real-Time Systems
Arrival curves for real-time calculus: the causality problem and its solutions
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Combining network calculus and scheduling theory to improve delay bounds
Proceedings of the 20th International Conference on Real-Time and Network Systems
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Real-Time Calculus (RTC) [14] is a framework to analyze heterogeneous real-time systems that process event streams of data. The streams are characterized by arrival curves which express upper and lower bounds on the number of events that may arrive over any specified time interval. System properties may then be computed using algebraic techniques in a compositional way. The property of causality on arrival curves essentially characterizes the absence of deadlock in the corresponding generator. A mathematical operation called causality closure transforms arbitrary curves into causal ones. In this paper, we extend the existing theory on causality to the class Upac of infinite curves represented by a finite set of points plus piecewise affine functions, where existing algorithms did not apply. We show how to apply the causality closure on this class of curves, prove that this causal representative is still in the class and give algorithms to compute it. This provides the tightest pair of curves among the curves which accept the same sets of streams.