Network calculus

Network calculus

Network calculus is a mathematical framework used to analyze and predict the behavior of computer networks. It involves the use of arrival and departure curves to determine the traffic delay in a network. This approach is often used to calculate an upper bound of delays in network communication.From: Model-Based Design for Embedded Systems [2019], Industrial Engineering and Manufacturing Technology [2015], Response time evaluation of industrial-scale distributed control systems by discrete event systems formalisms [2022]

Dimensioning of Civilian Avionics Networks

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Published in Richard Zurawski, Industrial Communication Technology Handbook, 2017

Jean-Luc Scharbarg, Christian Fraboul

Network calculus is mathematically based on the (min, +) dioid, for which the convolution ⊗ and the deconvolution Ø are defined as follows: (f⊗g)(t)=inf0≤u≤t(f(t−u)+g(u))and(f∅g)(t)=sup0≤u(f(t+u)−g(u))

Response time evaluation of industrial-scale distributed control systems by discrete event systems formalisms

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Published in International Journal of Control, 2022

Ouail Himrane, Alain Ourghanlian, Saïd Amari

Over the past few years, a number of research efforts have been undertaken in order to evaluate the end-to-end delays of NCS (delay experienced by a packet when traversing the network) as in Bauer et al. (2010) and Georges et al. (2011). These approaches are based, in particular, on Network Calculus (Boudec & Thiran, 2001; Cruz, 1991) or Trajectory Approach (Martin & Medlej, 2015) to calculate an upper bound of these delays. Moreover, congestion control is also considered in Liu et al. (2013) to avoid packets drop.

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Dimensioning of Civilian Avionics Networks

Response time evaluation of industrial-scale distributed control systems by discrete event systems formalisms