Modern society greatly relies on a secure energy supply for communication, security, health care and many more applications. Just rarely do we experience blackouts that make us aware of our...Show moreModern society greatly relies on a secure energy supply for communication, security, health care and many more applications. Just rarely do we experience blackouts that make us aware of our dependence on the various components of the power network. However, the power network was not designed to supply the ever-increasing demand that it faces today and without changes this will lead to more blackouts in the future. This thesis focusses on reducing the damage caused by cascading failures – failures that induce new failures and ultimately lead to a blackout. Concretely, we zoom in on a part of the power network – the high voltage power grid – and study intentional islanding, a mechanism that reduces the damage done by cascading failures. Intentional islanding separates the network in two or more components in order to isolate a cascading failure. This should protect the rest of the network from serious damage, although islanding by itself may also cause a wide disturbance. In this thesis, intentional islands are designed by formulating a MILP optimization problem that takes into consideration various trade-offs in islands design such as stability and load shed. To test the islanding mechanism introduced in this thesis, we want to create instances with cascading failures. For this, it is essential to know which transmission lines are most important to the power grid’s robustness. The relative importance of individual transmission lines to the power grid is calculated and used to simulate cascading failures. Both damage done by the cascading failures and general grid safety are analyzed with and without the implementation of islanding. Our results show that intentional islanding can be a very effective mechanism to protect the grid if implemented correctly.Show less
Coverability sets can be very useful in the analysis of Petri nets. For P/T nets, an algorithm for construction of these sets is known. For P/T nets extended with inhibitor arcs (PTI nets) no such...Show moreCoverability sets can be very useful in the analysis of Petri nets. For P/T nets, an algorithm for construction of these sets is known. For P/T nets extended with inhibitor arcs (PTI nets) no such algorithm exists. This thesis consists of three parts. The first part analyses the standard algorithm for coverability sets, and provides some methods to extract a more representative set from the result. In the second part, we prove that for every Petri net, a unique finite minimal coverability set exists. The last part focuses on PTI nets, and some ways to convert them back to P/T nets in such a way that coverability information is preserved.Show less
Om zeker te weten dat je kan eten in een restaurant, reserveert bijna iedere Nederlander een tafeltje. Weinig mensen kiezen ervoor om zonder te reserveren naar een restaurant te gaan. Maar is dit...Show moreOm zeker te weten dat je kan eten in een restaurant, reserveert bijna iedere Nederlander een tafeltje. Weinig mensen kiezen ervoor om zonder te reserveren naar een restaurant te gaan. Maar is dit wel beter? Is het niet veel beter om zonder te reserveren naar een restaurant te gaan en te gokken dat er een tafeltje vrij is? In dit verslag zullen we laten zien dan reserveren in sommige situaties beter is. Dus dat bij bepaalde voorwaarden geldt dat niet reserveren beter is en dat bij andere voorwaarden reserveren beter is. Het hoofddoel van dit verslag is het bewijs dat reserveren beter is onder bepaalde voorwaarden. Ook laat ik zien dat er een speciaal geval is dat het niet uitmaakt of je wel of niet reserveert.Show less
In this thesis1 a direct generalisation of the recombining binomial model by Cox, Ross, and Rubinstein [16] based on Pascal’s simplex is constructed. This discrete method approximates the price of...Show moreIn this thesis1 a direct generalisation of the recombining binomial model by Cox, Ross, and Rubinstein [16] based on Pascal’s simplex is constructed. This discrete method approximates the price of derivatives on multiple assets in a Black-Scholes market environment. It consists of a sequence of recombining multinomial trees based on Pascal’s simplex. The generalisation keeps most aspects of the binomial model intact, of which the following are the most important: The direct link to Pascal’s simplex; the matching of the moments of the log-transformed process; and the completeness of the model. The goal of this thesis is to privide a theoretical satisfactory solution. However, the recombining multinomial model might also have the potential to provide a practical satisfactory solution.Show less
In this thesis we use mathematical models to dimension clouds. We focus on loss models from the theory of queueing. We use the blocking probability in these models as performance measure of a cloud...Show moreIn this thesis we use mathematical models to dimension clouds. We focus on loss models from the theory of queueing. We use the blocking probability in these models as performance measure of a cloud. We consider both infinite and finite source models as well as single-rate and multi-rate models for cloud dimensioning based on request blocking probability. These models enable providers to dimension both public and private clouds as well as clouds with one customer type and clouds with different customer types. In addition to surveying existing formulas, we also derive new formulas that can be used in practice. We also compare the different models and give recommendations about which model should be used in different cloud situations. Finally, we give a first quantification of the possible benefits of intercloud, the cooperation between cloud providers.Show less
