Introduction to algorithms
IEEE/ACM Transactions on Networking (TON)
Modern heuristic techniques for combinatorial problems
IEEE/ACM Transactions on Networking (TON)
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
A fast computational algorithm for the Legendre-Fenchel transform
Computational Optimization and Applications
Towards real-time measurement of traffic control parameters
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special Issue: performance modeling and evaluation of ATM networks
Performance Guarantees in Communication Networks
Performance Guarantees in Communication Networks
Network calculus: a theory of deterministic queuing systems for the internet
Network calculus: a theory of deterministic queuing systems for the internet
A dual approach to network calculus applying the legendre transform
QoS-IP'05 Proceedings of the Third international conference on Quality of Service in Multiservice IP Networks
Slope transforms: theory and application to nonlinear signalprocessing
IEEE Transactions on Signal Processing
An Algorithmic Toolbox for Network Calculus
Discrete Event Dynamic Systems
New perspectives on network calculus
ACM SIGMETRICS Performance Evaluation Review
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Network calculus is a theory of deterministic queuing systems that has successfully been applied to derive performance bounds for communication networks. Founded on min-plus convolution and de-convolution, network calculus obeys a strong analogy to system theory. Yet, system theory has been extended beyond the time domain applying the Fourier transform thereby allowing for an efficient analysis in the frequency domain. A corresponding dual domain for network calculus has not been elaborated, so far.In this paper we show that in analogy to system theory such a dual domain for network calculus is given by convex/ concave conjugates referred to also as the Legendre transform. We provide solutions for dual operations and show that min-plus convolution and de-convolution become simple addition and subtraction in the Legendre domain. Additionally, we derive expressions for the Legendre domain to determine upper bounds on backlog and delay at a service element and provide representative examples for the application of conjugate network calculus.