In this paper we introduce a new kind of game, called a deck building game, of which Dominion is the most prominent example. We focus on the question to what extent traditional game analysis...Show moreIn this paper we introduce a new kind of game, called a deck building game, of which Dominion is the most prominent example. We focus on the question to what extent traditional game analysis techniques can be used to analyze deck building games? To do this, we look at several simple strategies, like Random and Greedy, and some traditional techniques, namely Monte Carlo Tree Search and Dynamic Programming. We compare the strategies for mid (31 turns) to long games (100 turns). We conclude that our implementation of DP seems to be suitable only for games of medium length or shorter because of its space complexity, whereas our implementation of MCTS seems to fall behind other strategies with similar performance in regards of time complexity.Show less
Menigeen heeft wel eens gehoord van het `lights out'-probleem. Over dit probleem is een hoop op internet te vinden, met name met verscheidene roosters, zogenaamde `grids'. Het idee hiervan is dat...Show moreMenigeen heeft wel eens gehoord van het `lights out'-probleem. Over dit probleem is een hoop op internet te vinden, met name met verscheidene roosters, zogenaamde `grids'. Het idee hiervan is dat je een heel rooster, bestaande uit lampjes die ofwel aan ofwel uit staan, vanuit een semi-willekeurige configuratie volledig uit kunt krijgen door goed gekozen lampjes van toestand te laten veranderen, waarbij de volgende eigenschap geldt: Als lampje X van toestand verandert, oftewel van uit naar aan gaat, of van aan naar uit, dan zullen alle aangrenzende lampjes van X tevens van toestand veranderen.Show less
Iedereen heeft zichzelf wel eens in een situatie bevonden waarin ´e´en of meerdere goederen verdeeld moesten worden over een aantal mensen. Bij zo’n verdeling wil iedereen het liefst het grootste...Show moreIedereen heeft zichzelf wel eens in een situatie bevonden waarin ´e´en of meerdere goederen verdeeld moesten worden over een aantal mensen. Bij zo’n verdeling wil iedereen het liefst het grootste deel hebben. Laten we het voor het gemak over een cake hebben, dan is het doel dus om de cake zo te verdelen dat iedereen een stuk krijgt waar hij tevreden mee is. In dit onderzoek wordt naar dergelijke problemen gekeken: Wanneer is een gegeven verdeling eerlijk? Eerst zal beschreven worden wanneer een verdeling eerlijk genoemd mag worden. Hierna wordt naar het eenvoudige probleem gekeken van een verdeling over twee personen en daarna naar het complexe probleem van een verdeling over meer dan twee personen. Voor beide problemen zal een procedure uitgebreid besproken worden; een procedure die een verdeling oplevert waarmee iedereen tevreden is. Om een goed beeld te krijgen van de beschreven procedures, zullen voldoende (toelichtende) voorbeelden gegeven worden. In werkelijkheid komt het vaak voor dat mensen liegen om op die manier een groter deel van (bijvoorbeeld) de cake te krijgen, ook hiernaar zal dus gekeken worden. Het doel van dit onderzoek is om een beeld te krijgen van hoe verdelingen van ´e´en of meer goederen bereikt kunnen worden op een zo eerlijke mogelijke manier. Tijdens dit onderzoek is gebruik gemaakt van de hoofdstukken 5 en 11 uit het boek ‘Mathematics and Politics - Stratery, Voting, Power and Proof’ van Alan D. Taylor en Allison M. Pacelli.[1] De stellingen, algoritmes en bewijzen uit deze hoofdstukken zijn wiskundig onvolledig, daarom zullen we in dit onderzoek proberen deze te verbeteren en correct te makenShow less
In this thesis, we will compare two different methods for computing the stationary probabilities of Quasi-Birth-Death processes. The first method is Lattice Path Counting, as described in [1] and ...Show moreIn this thesis, we will compare two different methods for computing the stationary probabilities of Quasi-Birth-Death processes. The first method is Lattice Path Counting, as described in [1] and [2], the second Successive Lumping, which is explained in detail in [3]. We begin by explaining what a Quasi-Birth-Death process is and why it’s so hard to calculate its steady state probabilities. After that, a short description follows of both methods. We will briefly explain how they work and in which cases they can be used. These descriptions are meant as a short introduction to the workings of these methods. A more in depth explanation and more formal proofs can be found in the respective articles in which the methods are introduced. After that, both methods will be applied to a number of examples to show that the Successive Lumping method is applicable in more situations than Lattice Path Counting. Readers are expected to have a basic understanding of both discrete- and continuous-time Markov chains.Show less
The structure of the power grid has been unchanged since the introduction of AC power. With the introduction of clean energy we see that the purpose of the grid changes. Instead of only having...Show moreThe structure of the power grid has been unchanged since the introduction of AC power. With the introduction of clean energy we see that the purpose of the grid changes. Instead of only having large power plants, we now have many small generators scattered over the grid. The power network was not designed for this amount of distributed generation and our ever increasing demand for energy. Therefore we can expect that this trend will lead to an increase of interruptions due to a new kind of failures. In this thesis we will investigate the use of temperature and current measurements to prevent these failures from happening unexpectedly and how we can reduce the return on investment time of cables. In this thesis we will investigate the distribution system operator and the challenges found in the distribution grid of Westland Infra. We will simulate a small part of the distribution grid. We will evaluate important parameters for the challenges in the grid of Westland Infra and we will develop a proactive maintenance policy to reduce the return on investment time of adding cables in the grid.Show less
In deze bachelorscriptie worden verschillende indices besproken die de competitiviteit, de mate van onvoorspelbaarheid, van een sporttoernooi kwantificeren. Hierbij wordt gebruik gemaakt van een...Show moreIn deze bachelorscriptie worden verschillende indices besproken die de competitiviteit, de mate van onvoorspelbaarheid, van een sporttoernooi kwantificeren. Hierbij wordt gebruik gemaakt van een vooraf bepaalde ranking van de deelnemers en de uitslagen van het gespeelde toernooi, waarbij gelijkspel buiten beschouwing wordt gelaten. De indices die behandeld zullen worden zijn de (optimale) toernooi-index, Slater’s i, Kendall’s τ , het competitief evenwicht en de gewogen toernooi-index. Daarnaast zullen relaties tussen de (optimale) toernooi-index, Slater’s i en Kendall’s τ gegeven worden, waarna een mooi resultaat besproken wordt. Tot slot wordt aan de hand van de dynamische ranking, gebaseerd op de win-verlies score, besproken hoe de vooraf vastgestelde ranking bepaald kan worden.Show less
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
This thesis introduces the successive lumping procedure (SLP) to compute the steady state probabilities for a class of Markov Chains with large state spaces. In this procedure we introduce one or...Show moreThis thesis introduces the successive lumping procedure (SLP) to compute the steady state probabilities for a class of Markov Chains with large state spaces. In this procedure we introduce one or multiple successive lumping states processes. Also, this thesis studies the classical reorder quantity, order point (Q, r) continuous review stochastic inventory model. This model has been extensively studied in the literature and its use in practice is widespread. Using the SLP efficient calculations can be done for this model when there are Bernoulli arrivals, a mixture of backorders, lost sales and a random lead time. In addition, this work extends previous research in this area by providing efficient algorithms for the computation of the optimal (Q∗ , r∗ ) values when there are Poisson arrivals, a multi-breakpoint discount pricing structure and a fixed lead time.Show less
This thesis describes the research done at the BC Cancer Agency in Vancouver, Canada, as part of a CIHR-team, using operations research to solve health care problems. Appointment booking data is...Show moreThis thesis describes the research done at the BC Cancer Agency in Vancouver, Canada, as part of a CIHR-team, using operations research to solve health care problems. Appointment booking data is used to determine where problems occur in the Chemo unit. One of these problems is the mismatch of capacity and demand. Some days there is slack capacity and other days appointments need to be rescheduled due to lack of capacity. A Markov Decision Process of the process is introduced and via Markov Chain theory a simulation model is introduced. New booking methods and ways to add capacity are tested using this simulation model. We conclude that using a booking method that is a bit more advanced and uses the booking tolerance earlier in the process gives the best results, and is significantly better than adding extra capacity.Show less
