Exposés de synthèse

Titre de l’exposé : Challenges in the Stochastic Modeling of Service Systems: Illustrations with Call Centers (transparents)

Résumé : Large systems that involve humans (such as health-care systems, call centers, emergency systems, transportation networks, supply chains, communication systems, etc.) are difficult to manage because they are complex and involve significant uncertainty which is itself hard to model in a realistic way. For example, call arrivals in call centers follow stochastic processes whose rates are themselves random and depends significantly on the time of the day, type of day (day of the week, holiday), period of the year, weather, other external events, etc. The arrival processes of different call types may also be dependent. Call durations (service times) have distributions that depend on the call type and on the particular agent who handles the call, and are often time-dependent because the effectiveness of agents depends on their experience, base qualities, motivation, fatigue, etc. Similar complications occur in other systems mentioned above. As a result, valid and reliable stochastic models for these systems are hard to build and maintain. They require continuous learning and adaptation based on incoming data that reflects system evolution.

The main motivation for modeling and simulating these systems is to construct good decision-making policies for their management. In a typical call center with multiple call types and multiple agent types (who can handle subsets of call types), one must decide how many agents to hire and train, for what call types, construct work schedules for these agents that respect union agreements, specify dynamic routing rules for arriving calls and for agents that become available, while meeting certain (stochastic) constraints on the quality of service of the systems (e.g., on the distributions of waiting times and call abandonments), and dothis at the least possible cost. Solving such stochastic optimization problems via simulation, both for long- and medium-term planning (days or months in advance) and for short-term decision making and recourse to face unexpected situations, are challenging tasks.

We will illustrate these types of modeling and optimization problems with concrete examples and data, and will review some recent models and ideas.

Titre de l’exposé : Réseaux de Whittle et applications (transparents)

Résumé : Les réseaux de Whittle sont un outil puissant et pourtant peu connu de la théorie des files d’attente, généralisant les réseaux de Jackson et les réseaux de Kelly. Ils permettent de représenter certaines dépendances entre les taux de service des différentes files d’attente du réseau tout en gardant une forme explicite de la distribution stationnaire. Cet exposé constituera une introduction à cette classe de réseaux de files d’attente. Nous en donnerons la définition et les principales propriétés, puis montrerons en quoi ils permettent d’obtenir très simplement certains résultats classiques de la théorie des files d’attente, comme l’insensibilité de la discipline de service « processeur partagé ». Nous terminerons l’exposé par les applications des réseaux de Whittle aux problèmes d’ingénierie des réseaux de communication et des centres de données.

Titre de l’exposé : Algorithms for and from network calculus (transparents)

Résumé : Network caluclus (NC) is a theory based on the (min,plus) algebra and whose aim is to compute worst-case performance bounds in communication networks. This theory abstracts flows circulating in a network and the service offered by the networks elements by functions on which computations are performed. After a review of the basics of the theory, two problems will be addressed. First the problem of computing exact worst-case performance bounds in a feed-forward network, and second, the problem of supervision of a flow that uses some basic concept of NC but with a different aim.