The paper is designated to the analysis of queueing systems, arising in the network theory and communications theory (called multiphase queueing systems, tandem queues or series of queueing systems). Also we note that multiphase queueing systems can be useful for modelling practical multi-stage service systems in a variety of disciplines, especially on manufacturing (assembly lines), computer networking (packet switch structures), and in telecommunications (e.g. cellular mobile networks), etc. This research presents heavy traffic limit theorems for the cumulative idle time in multiphase queues. In this work, functional limit theorems are proved for the values of important probability characteristics of the queueing system (a cumulative idle time of a customer).

Nous présentons dans cet article un algorithme générique hybride permettant de combiner des méthodes complètes (programmation par contraintes) et incomplètes(recherche locale) pour la résolutionde problèmes de satisfaction de contraintes.Ce schéma algorithmique basé sur la gestion de populations, utilise destechniques de propagation de contraintes intégrant également des heuristiques de recherche locale. Les structures utiliséesautorisent une interaction homogène entre les différentes méthodes mises enœuvre et permettent également de bénéficier de leurs atoutsrespectifs. Nous proposons alors diverses stratégies de combinaisons dont nous mettons en avant l'intérêt sur quelques exemples par lebiais d'une implémentation.

We consider the Airspace Sectorization Problem (ASP) in which airspacehas to be partitioned into a given number of sectors, each of whichbeing assigned to a team of air traffic controllers. The objective isto minimize the coordination workload between adjacent sectors whilebalancing the total workload of controllers. Many specificconstraints, including both geometrical and aircraft relatedconstraints are taken into account. The problem is solved in aconstraint programming framework. Experimental results show that ourapproach can be used on real life problems.

This paper introduces a new method to prune the domains of the variablesin constrained optimization problems where the objective function is defined by a sumy = ∑xi , and where the integer variables x i are subject to difference constraintsof the form xj - xi ≤ c. An important application area where such problems occur is deterministic scheduling with the mean flow time as optimality criteria.This new constraint is also more general than a sum constraint defined on a set of ordered variables. Classical approaches perform a local consistency filtering after each reduction ofthe bound of y. The drawback of these approaches comes from the fact that the constraints are handled independently.We introduce here a global constraint that enables to tackle simultaneously the whole constraint system, and thus, yields a more effective pruningof the domains of the x i when the bounds of y are reduced.An efficient algorithm,derived from Dijkstra's shortest path algorithm, is introduced to achieve interval consistency on this global constraint.