Le calcul reseau (network calculus) est une theorie basee sur l’algebre min-plus. Il offre un cadre formel de modelisation des reseaux de communication. Il a ete utilise pour certifier le reseau AFDX embarque dans l’A380 de Airbus. Seulement, les bornes sur le delai annonces par ces travaux de certification souffrent d’une sur-approximation dans le cas precis de l’agregation dans un contexte de priorite statique non preemptive.L’objectif de nos travaux est de reduire cette sur-approximation. Dans cette these, nous proposons un service residuel permettant d’obtenir de meilleurs bornes sur le delai dans le cas de la politique a priorite statique non preemptive et de la politique DRR. Nous montrons aussi comment ces deux politiques peuvent etre combinees dans une politique hierarchique a deux niveaux.

Le calcul réseau (network calculus) est une théorie basée sur l’algèbre min-plus. Il offre un cadre formel de modélisation des réseaux de communication. Il a été utilisé pour certifier le réseau AFDX embarqué dans l’A380 de Airbus. Seulement, les bornes sur le délai annoncés par ces travaux de certification souffrent d’une sur-approximation dans le cas précis de l’agrégation dans un contexte de priorité statique non préemptive.L’objectif de nos travaux est de réduire cette sur-approximation. Dans cette thèse, nous proposons un service résiduel permettant d’obtenir de meilleurs bornes sur le délai dans le cas de la politique à priorité statique non préemptive et de la politique DRR. Nous montrons aussi comment ces deux politiques peuvent être combinées dans une politique hiérarchique à deux niveaux.

GPS is an ideal well known policy designed to share the capacity of a server between the input flows: each flow receives a fractional part, defined by the administrator, of the total server capacity 1 . It has several practical implementations, like P-GPS. These policies have been defined in the context of a constant-rate server. In this paper, a generalisation of GPS and P-GPS is proposed, in network calculus, to any kind of service. This generalisation offers a suitable framework to combine scheduling policies: for example, having a first level of static priority scheduling, and sharing the residual service with a P-GPS policy.

The real-time behaviour of critical real-time systems relies on the real-time behaviour of the network and some method to compute bounds on the traversal time (worst case traversal time – WCTT). Network calculus (NC) is a method designed to compute such bounds, and one challenge is to have tight bounds, i.e. reaching the exact worst case, to avoid over-provisioning. In this paper, we present a new way to handle non-preemptive static priority (NP-SP) with NC, very accurate (it reaches the real worst cases in all thousands tested configurations), and to combine it with packet-based generalised processor sharing (P-GPS), providing bounds on NP-SP/P-GPS in network calculus1.

Generalised Processor Sharing (GPS) is a wellknown ideal service policy designed to share the capacity of a server among the input flows fairly: each backlogged flow receives a pre-defined fraction of the total server capacity, according to its weight. Several practical implementations of GPS have been proposed, among which Deficit Round Robin (DRR) is widely deployed since it can be implemented in a very efficient way. The worst-case performance of DRR has been studied by several papers, all of which assume that the shared server has a constant rate. This paper studies DRR using Network Calculus, under very general assumptions. Latency results that generalise all the previous works are derived, and a residual service is derived from DRR parameters. This residual service is shown to be as good as or even better than previous studies when restricting it to the same assumptions.

The paper addresses worst case performance analysis of non preemptive static scheduling priority scheduling within the network calculus theory. Previous studies have been done, each one generalizing some other [8,1,7,3,10], needing weaker hypotheses or improving accuracy of results. This paper presents a very general results, with an accuracy that appear, on preliminary examples, as good as all other one.