Abstract

In INterdomain Ingress Traffic Engineering (INITE), a “target” Autonomous System (AS) aims to control the ingress link at which the traffic of one or more upstream source networks enters that AS. In practice, ISPs often manipulate, mostly in a trial-and-error manner, the length of the AS-Path attribute of upstream routes through a simple technique known as prepending (or padding). In this paper, we focus on prepending and propose a polynomial-time algorithm (referred to as OPV) that determines the optimal padding for an advertised route at each ingress link of the target network. Specifically, given a set of “elephant” source networks and some maximum load constraints on the ingress links of the target AS, OPV determines the minimum padding at each ingress link so that the load constraints are met, when it is feasible to do so. OPV requires as input an AS-Path length estimate from each source network to each ingress link. We describe how to estimate this matrix, leveraging the BGP Looking Glass Servers. To deal with unavoidable inaccuracies in the AS-Path length estimates, and also to compensate for the generally unknown BGP tie-breaking process in upstream networks, we also develop a robust variation (RPV) of the OPV algorithm. Document type: Part of book or chapter of book

Abstract

In this report, we study the problem of optimizing the throughput of applications for heterogeneous platforms subject to failures. The considered applications are composed of a sequence of consecutive tasks linked as a linear graph (pipeline), with a type associated to each task. The challenge is to specialize the machines of a target platform to process only one task type, given that every machine is able to process all the types before being specialized, to avoid costly context or setup changes. Each instance can thus be performed by any machine specialized in its type and the workload of the system can be shared among a set of specialized machines. For identical machines, we prove that an optimal solution can be computed in polynomial time. However, the problem becomes NP-hard when two machines can compute the same task type at different speeds. Several polynomial time heuristics are presented for the most realistic specialized settings. Experimental results show that the best heuristics obtain a good throughput, much better than the throughput obtained with a random mapping, and close to the optimal throughput in the particular cases on which the optimal throughput can be computed.; Dans ce rapport, nous étudions le problème de l'optimisation du débit d'applications de type pipeline dans un environnement hétérogène sujet à des pannes. Les applications sont constituées d'un ensemble de tâches consécu\\-tives typées et organisées selon une chaîne linéaire ou pipeline. Le but est ici de spécialiser les machines de la plate-forme d'exécution afin qu'elles ne traitent qu'un seul type de tâches, sachant qu'au départ elles peuvent exécuter tous les types. Cela permet d'éviter des reconfigurations coûteuses entre tâches de types différents sur une même machine. Ainsi, les instances d'une même tâche peuvent être distribuées sur plusieurs machines spécialisées pour le type de cette tâche, ce qui permet une répartition de la charge du système sur un ensemble de machines spécialisées. Lorsque la plate-forme est composée de machines identiques, nous prouvons qu'une solution optimale peut être trouvée en temps polynomial. Par contre, le problème devient NP-complet dès lors que deux machines peuvent traiter une même tâche à des vitesses différentes. Ce faisant, plusieurs heuristiques sont présentées dans le cas le plus réaliste d'un système spécialisé. Les résultats expérimentaux montrent que les meilleures heuristiques obtiennent de bons résultats en terme de débit, meilleurs qu'avec une allocation aléatoire, et que les débits atteints sont très proches des débits optimaux dans les cas particuliers pour lesquels une solution optimale peut être calculée. Document type: Part of book or chapter of book

Abstract

Probabilistic model checking mainly concentrates on techniques for reasoning about the probabilities of certain path properties or expected values of certain random variables. For the quantitative system analysis, however, there is also another type of interesting performance measure, namely quantiles. A typical quantile query takes as input a lower probability bound p and a reachability property. The task is then to compute the minimal reward bound r such that with probability at least p the target set will be reached before the accumulated reward exceeds r. Quantiles are well-known from mathematical statistics, but to the best of our knowledge they have not been addressed by the model checking community so far. In this paper, we study the complexity of quantile queries for until properties in discrete-time finite-state Markov decision processes with non-negative rewards on states. We show that qualitative quantile queries can be evaluated in polynomial time and present an exponential algorithm for the evaluation of quantitative quantile queries. For the special case of Markov chains, we show that quantitative quantile queries can be evaluated in time polynomial in the size of the chain and the maximum reward. Document type: Part of book or chapter of book