This is the first book that analyses the future raw materials supply from the demand side of a society that chiefly relies on renewable energies, which is of great significance for us all. It addresses primary and secondary resources and substitution, not only from technical but also socioeconomic and ethical points of view. The "Energiewende" (Energy Transition) will change our consumption of natural resources significantly. When in future our energy requirements will be covered mostly by wind, solar power and biomass, we will need less coal, oil and natural gas. However, the consumption of minerals, especially metallic resources, will increase to build wind generators, solar panels or energy storage facilities. Besides e.g. copper, nickel or cobalt, rare earth elements and other high-tech elements will be increasingly used. With regard to primary metals, Germany is 100 % import dependent; only secondary material is produced within Germany. Though sufficient geological primary resources exist worldwide, their availability on the market is crucial. The future supply of the market is dependent on the development of prices, the transparency of the market and the question of social and ethical standards in the raw materials industry, as well as the social license to operate, which especially applies to mining. The book offers a valuable resource for everyone interested in the future raw material supply of our way of life, which will involve more and more renewable energies.

Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models.

The goal of input modeling is to find a stochastic model to describe a sequence ofmeasurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published.

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This is the first book that analyses the future raw materials supply from the demand side of a society that chiefly relies on renewable energies, which is of great significance for us all. It addresses primary and secondary resources and substitution, not only from technical but also socioeconomic and ethical points of view. The "Energiewende" (Energy Transition) will change our consumption of natural resources significantly. When in future our energy requirements will be covered mostly by wind, solar power and biomass, we will need less coal, oil and natural gas. However, the consumption of minerals, especially metallic resources, will increase to build wind generators, solar panels or energy storage facilities. Besides e.g. copper, nickel or cobalt, rare earth elements and other high-tech elements will be increasingly used. With regard to primary metals, Germany is 100 % import dependent; only secondary material is produced within Germany. Though sufficient geological primary resources exist worldwide, their availability on the market is crucial. The future supply of the market is dependent on the development of prices, the transparency of the market and the question of social and ethical standards in the raw materials industry, as well as the social license to operate, which especially applies to mining. The book offers a valuable resource for everyone interested in the future raw material supply of our way of life, which will involve more and more renewable energies.

Logistik spielt eine entscheidende Rolle fur unsere Volkswirtschaft. Logistik-Netze werden jedoch aufgrund steigender Anforderungen immer grosser, komplexer und damit schwerer zu planen und zu beherrschen. Dafur sind Methoden der Analyse, Planung und Optimierung erforderlich. In diesem Band werden neue Methoden zur Planung und zum Betrieb grosser Netze dargestellt, die Wissenschaftler aus den Bereichen Logistik, Informatik, Betriebswirtschaftslehre, Statistik und Soziologie gemeinsam entwickelt und auf praxisnahe Beispiele angewendet haben."

Das Buch behandelt die quantitative Analyse komplexer dynamischer Systeme mittels Modellen, die sich auf Markov-Prozesse abbilden lassen. Es wird ein Konzept entwickelt, welches die hierarchische Spezifikation von komplexen Modellen und die Kombination verschiedener bekannter Modellierungsparadigmen in einem Modell erlaubt. Neue Analysetechniken werden vorgestellt, die unter Ausnutzung der Modellstruktur eine sehr effiziente Modellanalyse erm-glichen. Im Vergleich zu bekannten Analysetechniken lassen sich deutlich gr- ere Modelle analysieren und in vielen F{llen wird auch der Zeitaufwand der Analyse drastisch gemindert. Bei Vorliegen spezieller Modelleigenschaften, wie sie insbesondere bei Multiprozessorsystemen oder Rechnernetzen vorliegen, ist eine Reduzierung des zu analysierenden Markov-Prozesses mittels Aggregierung m-glich, ohne die Exaktheit der Resultate zu beeinflussen. Dar}ber hinausgehende Vereinfachungen deszu analysierenden Systems, die zu approximativen Ergebnissen f}hren, sind mit Hilfe der neuen Analysealgorithmen ebenfalls m-glich.