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R\u00e9sum\u00e9 : 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.<\/p>\n
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.<\/p>\n
We will illustrate these types of modeling and optimization problems with concrete examples and data, and will review some recent models and ideas.<\/p>\n
R\u00e9sum\u00e9 : Les r\u00e9seaux de Whittle sont un outil puissant et pourtant peu connu de la th\u00e9orie des files d’attente, g\u00e9n\u00e9ralisant les r\u00e9seaux de Jackson et les r\u00e9seaux de Kelly. Ils permettent de repr\u00e9senter certaines d\u00e9pendances entre les taux de service des diff\u00e9rentes files d’attente du r\u00e9seau tout en gardant une forme explicite de la distribution stationnaire. Cet expos\u00e9 constituera une introduction \u00e0 cette classe de r\u00e9seaux de files d’attente. Nous en donnerons la d\u00e9finition et les principales propri\u00e9t\u00e9s, puis montrerons en quoi ils permettent d’obtenir tr\u00e8s simplement certains r\u00e9sultats classiques de la th\u00e9orie des files d’attente, comme l’insensibilit\u00e9 de la discipline de service \u00ab\u00a0processeur partag\u00e9\u00a0\u00bb. Nous terminerons l’expos\u00e9 par les applications des r\u00e9seaux de Whittle aux probl\u00e8mes d’ing\u00e9nierie des r\u00e9seaux de communication et des centres de donn\u00e9es.<\/p>\n
R\u00e9sum\u00e9 : 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.<\/p>","protected":false},"excerpt":{"rendered":"
Pierre L’Ecuyer, Universit\u00e9 de Montr\u00e9al, chaire internationale Inria Titre de l’expos\u00e9 : Challenges in the Stochastic Modeling of Service Systems: Illustrations with Call Centers (transparents) R\u00e9sum\u00e9 : 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 … <\/p>\n