This thesis is concerned with studying the behavior of a gossiping protocol in the specific sense meant by Ericsson; in the following pages I’ll introduce a Markov process which models the spread of information in such systems. The results will be verified by means of a discreet-event simulation. / Gossiping Protocols, are inherently random in behavior.Nonetheless, they are not structure-less. Their asymptotic behavior when implemented in large scales is the matter of focus in this thesis. / Tel: +46709700505 Address: Pinnharvsgatan 3 E lgh 1202 43147 Mölndal Sweden

Accurate and reliable effort estimation is still one of the most challenging processes in software engineering. There have been numbers of attempts to develop cost estimation models. However, the evaluation of model accuracy and reliability of those models have gained interest in the last decade. A model can be finely tuned according to specific data, but the issue remains there is the selection of the most appropriate model. A model predictive accuracy is determined by the difference of the various accuracy measures. The one with minimum relative error is considered to be the best fit. The model predictive accuracy is needed to be statistically significant in order to be the best fit. This practice evolved into model evaluation. Models predictive accuracy indicators need to be statistically tested before taking a decision to use a model for estimation. The aim of this thesis is to statistically evaluate well known effort estimation models according to their predictive accuracy indicators using two new approaches; bootstrap confidence intervals and permutation tests. In this thesis, the significance of the difference between various accuracy indicators were empirically tested on the projects obtained from the International Software Benchmarking Standard Group (ISBSG) data set. We selected projects of Un-Adjusted Function Points (UFP) of quality A. Then, the techniques; Analysis Of Variance ANOVA and regression to form Least Square (LS) set and Estimation by Analogy (EbA) set were used. Step wise ANOVA was used to form parametric model. K-NN algorithm was employed in order to obtain analogue projects for effort estimation use in EbA. It was found that the estimation reliability increased with the pre-processing of the data statistically, moreover the significance of the accuracy indicators were not only tested statistically but also with the help of more complex inferential statistical methods. The decision of selecting non-parametric methodology (EbA) for generating project estimates in not by chance but statistically proved.

This thesis describes methods of secret communication based on latin squares and their close relative, quasigroups. Different types of cryptosystems are described, including ciphers, public-key cryptosystems, and cryptographic hash functions. There is also a chapter devoted to different secret sharing schemes based on latin squares. The primary objective is to present previously described cryptosystems and secret sharing schemes in a more accessible manner, but this text also defines two new ciphers based on isotopic latin squares and reconstructs a lost proof related to row-latin squares. / Denna uppsats beskriver kryptosystem och metoder för hemlighetsdelning baserade på latinska kvadrater och det närliggande konceptet kvasigrupper. Olika sorters chiffer, både symmetriska och asymmetriska, behandlas. Dessutom finns ett kapitel tillägnat kryptografiska hashfunktioner och ett tillägnat metoder för hemlighetsdelning. Huvudsyftet är att beskriva redan existerande metoder för hemlig kommunikation på ett mer lättillgängligt sätt och med nya exempel, men dessutom återskapas ett, till synes, förlorat bevis relaterat till rad-latinska kvadrater samt beskrivs två nya chiffer baserade på isotopa latinska kvadrater.

An area in graph theory is graph colouring, which essentially is a labeling of the vertices or edges according to certain constraints. In this thesis we consider star edge colouring, which is a variant of proper edge colouring where we additionally require the graph to have no two-coloured paths or cycles with length 4. The smallest number of colours needed to colour a graph G with a star edge colouring is called the star chromatic index of G and is denoted <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cchi'_%7Bst%7D(G)" />. This paper proves an upper bound of the star chromatic index of bipartite graphs in terms of the maximum degree; the maximum degree of G is the largest number of edges incident to a single vertex in G. For bipartite graphs Bk with maximum degree <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?k%5Cgeq1" />, the star chromatic index is proven to satisfy<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%20%5Cchi'_%7Bst%7D(B_k)%20%5Cleq%20k%5E2%20-%20k%20+%201" />. For bipartite graphs <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?B_%7Bk,n%7D" />, where all vertices in one part have degree n, and all vertices in the other part have degree k, it is proven that the star chromatic index satisfies <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cchi'_%7Bst%7D(Bk,n)%20%5Cleq%20k%5E2%20-2k%20+%20n%20+%201,%20k%20%5Cgeq%20n%20%3E%201" />. We also prove an upper bound for a special case of multipartite graphs, namely <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?K_%7Bn,1,1,%5Cdots,1%7D" /> with m parts of size one. The star chromatic index of such a graph satisfies<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cchi'_%7Bst%7D(K_%7Bn,1,1,%5Cdots,1%7D)%20%5Cleq%2015%5Clceil%5Cfrac%7Bn%7D%7B8%7D%5Crceil%5Ccdot%5Clceil%5Cfrac%7Bm%7D%7B8%7D%5Crceil%20+%20%5Cfrac%7B1%7D%7B2%7Dm(m-1),%5C,m%20%5Cgeq%205" />. For complete multipartite graphs where m &lt; 5, we prove lower upper bounds than the one above.

Trends such as increasing awareness of sustainable production, shorter product life cycles and personalised products create challenges for the mining industry. A solution to these challenges may be a functional product business model, where the provider sells the hardware’s function under a service contract and is responsible for delivering the combination of hardware and services over the duration of the contract. Under a functional product contract, it is of great importance to predict the availability performance of the hardware. For the mining company to strengthen its competitiveness even further, the reliability and maintainability are also crucial factors to reduce costs, maximise profits, minimise downtime, and improve forecasting of operating hours. The feasibility of performance modelling would be increased if it could be performed by a tool.In prior research related to the reliability of mining vehicles in underground mines, a research gap for drilling rigs was identified. The aim of the thesis was to build a prototype tool and develop a realistic test case to apply it to as a demonstration of how it can help mining vehicle (drilling vehicle) providers understand the impact of their failure modes, particularly from the perspective of providing those vehicles under functional product contracts. The focus was to develop a tool that can be accessible for decision makers within mine operating and mine vehicle provider companies who are not specialists in reliability and maintenance modelling.A simulation model was developed in JaamSim, a graphical user interface developed in Qt designer and the integration between them developed in the Python programming language. A realistic test case was constructed with the purpose of imitating a jumbo drill rig, specifically the Boomer M2 manufactured by Epiroc, used to develop tunnels in an underground mine. Three critical failure modes of the Boomer M2 were identified. Simulations of the test case show that the bent boom arm failure mode had greatest influence on the availability of the drill rig.The developed prototype tool demonstrates the value of decision support tools for measuring the impact of failure modes on functional product contracts and its potential for aiding their negotiation and adoption. The tool has a low complexity regarding usage which should increase its usefulness for decision makers. To increase the tools usefulness further, extending its flexibility of application to other mining vehicles and different maintenance policies has been identified as the next steps for future work.Key words:

The competition between manufacturing companies is constantlyincreasing. There is therefore a need for continuously improvingproduction control and production planning. The requirements arepartly founded on higher customer expectations on quality anddelivery precision. These requirements make manufacturing operationsmore demanding. To become more competitive, companies often turn tovirtual engineering tools with the intention of finding improvementsproposals that are not always completely obvious. The aim of this thesis work was to identify bottlenecks that limitsystem line production with the help of discrete event simulationand to identify improvement proposals that were able to reduce theproduction lead time. The work has been carried out at ABB inLudvika at the department for manufacturing the outer casing forpower transformers. The reliability of the study was ensured byusing a mixture of qualitative and quantitative data collectionmethods that complemented each other appropriately. Process mappingand collected data were the bases a simulation model, which is thebasis for the achieved work result. Analysis of the simulation results gave strong indications that aspecific operation in the production line needed to be improved andthe need to better balance operator capacity within the line. Theprocess mapping and data analysis highligthted the need for thecompany to work more with process standardisation. The finalimprovement proposals submitted to the company are intended toincrease the delivery precision and production capacity / Konkurrensen mellan tillverkande företag ökar ständigt, behovet avkontinuerlig effektivisering av produktionsstyrning och planering ärsåledes ett faktum. Tillverkning försvåras samtidigt då kunderförväntar sig allt mer kvalitativa och unika produkter med högleveransprecision. För att bli mer konkurrenskraftig vänder sig oftaföretag till virtuella hjälpmedel med avseendet att finnaförbättringsförslag som inte alltid är helt självklara. Syftet med arbetet var att identifiera eventuella flaskhalsar sombegränsar produktionen med hjälp av händelsestyrd simulering och attidentifiera förbättringsförslag som påverkar produktionskapaciteten.Arbetet har utförts på ABB i Ludvika vid avdelningen förtillverkning av ytterhöljet till transformatorer. Studienstillförlitlighet säkerställdes genom användandet av en blandningmellan kvalitativa och kvantitativa datainsamlingsmetoder somkompletterade varandra. Processkartläggning och datainsamling vargrunden för att ta fram en valid simuleringsmodell som var grund fördet uppnådda arbetsresultatet. Analys av simuleringsresultatet gav starka indikationer på att enspecifik operation i produktionen behövde justeras samt attföretaget behöver jobba med balansering av operatörs resurser föratt bättre möta kapacitetsbehovet. Utöver detta finns det ettfortsatt behov att arbeta med process standardisering. Deslutgiltiga förbättringsförslagen som lämnats till företaget ärvägledande för att öka leveransprecisionen ochproduktionskapaciteten.

The following project has been carried out in collaboration with Abstracta AB (AAB), a company based in Lammhult with specialization in sound landscapes for indoor environments. The company manufactures different types of products with sound-absorbing properties where sustainability and design are in great focus. A new product idea of the company is based on developing an A-classified discreetly designed wall absorber that is considered more as a "wall" than a "wall with mounted absorbent on". The purpose of the project was to develop the following product on a conceptual level. A main research question with two underlying issues was developed that served as a support during the project. Question 1: How can an A-rated discreetly designed sound wall absorber be developed? 1.a: How can an A-rated sound wall absorber be developed? 1.b: How can a sound wall absorber achieve a discreetness in its design? The project followed a product development process where the mainly focus was on concept development and concept testing. The concept was developed based on data collected from a literature study and with the use of a sound absorption calculator. A sound absorption test and an examination form regarding the discrete modeling and design of the absorbent were performed for the final concept that the project resulted in. The project showed that an A-rated discreetly designed sound wall absorber can be developed through a process where design-critical specifications that affect the absorber's discrete design control how the object can be modeled. Via a sound absorption calculator, concepts can be designed that theoretically indicate an A-rate while the design-critical specifications are not exceeded. Based on the concept, a prototype is manufactured that can undergo a sound absorption test to determine the absorbent's actual sound absorption capacity. Finally, an examination is made to analyze whether the absorbent is considered a discrete alternative or not. Based on the project's results, the work process proved to be advantageous as the concept indicated a sound absorption capacity that exceeded the requirements of the A-rating and at the same time obtained a discreet design and modeling. This was achieved in connection with the manufacturing materials achieving their technical specifications and a square meter cost lower than expected. Based on the project's results, the work process proved to be advantageous as the concept indicated a sound absorption capacity that exceeded the requirements of the A-rating and at the same time obtained a discreet design and modeling. This was achieved in connection with the manufacturing materials achieving their technical specifications and a square meter cost lower than expected. In the further development of the final concept, a solution for how the absorbent is to be mounted on the wall must be developed as this was not focused on in the project based on its boundaries. To achieve a valid A-rate, an additional sound absorption test must also be performed where a larger object area of 10–12 m2 is tested. In future work, the concept's discrete modeling and design should also be examined based on physical treatment to review how the examination form's response results relate to this. / Följande projekt utförs i samarbete med Abstracta AB (AAB), ett företag som är stationerat i Lammhult och är specialiserade inom ljudlandskap för inomhusmiljöer. Företaget framställer olika typer av produkter med ljudabsorberande egenskaper där hållbarhet och design även är i stort fokus. En ny produktidé av företaget grundar sig i att utveckla en A-klassificerad diskret utformad väggabsorbent som betraktas mer som en ”vägg” än en ”vägg med uppmonterad absorbent på”. Syftet med projektet var att framta följande produkt på en konceptuell nivå. En huvudsaklig forskningsfråga med två underliggande frågeställningar togs fram som fungerade som ett stöd under projektets gång. Fråga 1: Hur kan en A-klassificerad diskret utformad ljudväggabsorbent utvecklas? 1.a: Hur kan en A-klassificerad ljudväggabsorbent utvecklas? 1.b: Hur kan en ljudväggabsorbent uppnå en diskrethet i sin design? Projektet följde en produktutvecklingsprocess där det största fokuset låg på konceptutvecklingen och koncepttestningen. Koncepten utvecklades utifrån insamlade data från en litteraturstudie och med användning av en ljudabsorptionskalkylator. Ett ljudabsorptionstest och ett undersökningsformulär gällande absorbentens diskreta utformning och design utfördes för det slutgiltiga konceptet som projektet resulterade i. Projektet visade att en A-klassificerad diskret utformad ljudväggabsorbent kan utvecklas genom en process där designkritiska specifikationer som berör absorbentens diskreta utformning styr hur objektet kan formges. Via en ljudabsorptionskalkylator kan koncept designas som teoretiskt indikerar en A-klassning samtidigt som de designkritiska specifikationerna ej överskrids. Utifrån konceptet tillverkas en prototyp som kan genomgå ett ljudabsorptionstest för att fastställa absorbentens verkliga ljudupptagningsförmåga. En undersökning görs slutligen för att analysera huruvida absorbenten betraktas som ett diskret alternativ eller ej. Utifrån projektets resultat visade sig arbetsprocessen vara fördelaktig då konceptet påvisade en ljudabsorptionsförmåga som överträffade A-klassningens krav och samtidigt erhöll en diskret utformning och design. Detta åstadkom i samband med att tillverkningsmaterialen uppnådde sina tekniska specifikationer och en kvadratmeterkostnad lägre än väntat. I fortsatt utveckling av det slutgiltiga konceptet måste en lösning till hur absorbenten ska monteras på väggen tas fram eftersom detta inte fokuserades på i projektet utifrån dess avgränsningar. För att en giltig A-klassificering ska nås måste även ytterligare ett ljudabsorptionstest utföras där en större objektarea på 10–12 m2 testas. I framtida arbete bör även konceptets diskreta utformning och design undersökas utifrån fysiska bemötanden för att granska hur undersökningsformulärets svarsresultat förhåller sig till detta.

LKAB hanterar en av världens största malmkroppar vid en underjordsgruva i Kiruna. I samband med deras gruvbrytning uppstår stora mängder avfall som måste hanteras korrekt. De avfallsanläggningar som finns på området har idag platsbrist, därför finns incitament att bygga nya anläggningar. Inför utformningen av dessa nya anläggningar behöver avfallsflöden inventeras och analyseras. I detta arbete har det skett med diskret händelsesimulering baserad på historisk data. På grund av osäkra parametrar har flera scenarion tagits fram. Utformningen av anläggningarna beror på vilken kapacitet de förväntas ha, vilket är beroende av hur ofta anläggningarna ska tömmas och hur mycket avfall som förväntas uppstå på gruvområdet. För att sedan hitta bästa möjliga placering på de nya anläggningarna har ett modifierat anläggningslokaliseringsproblem tillämpats. Den optimala placeringen är i den norra delen av gruvområdet och minskar den totala körsträckan. Placeringen påverkas inte av större flöden. / In Kiruna the company LKAB has an underground mine with one of the largest iron ore quantities in the world. When producing the iron ore, a lot of waste arise that has to be taken care of in a correct way. Due to lack of space in todays waste facilities, there exists incentives to build new ones. To be able to design these new facilities, the flows of waste has to be investigated and analyzed. This has been done by discrete-event simulation based on historical data. Since some of the collected parameters are uncertain, different scenarios have been tested. The design of the facilities are dependent on what capacity they are expected to store, which is dependent on how often the facilities will be emptied and how large quantities will arise in the mining area. To find an optimal placement for the new facilities, a modified facility location problem has been implemented. The optimal placement is in the north part of LKAB’s mining area and will lower the total driving distance. The optimal placement will not be affected by larger flows.

This master thesis has been performed in association with Blekinge Institute of Technology and in collaboration with the company Dynapac Compaction Equipment AB. The thesis aims to investigate how Discrete Event Simulation (DES) can be used for value and sustainability design concept assessments in early design stages. The research is made by investigating the example of simulating the lifecycle of a double drum asphalt compactor. The model is created in the computerbased DES software Simio LLC, where the captured data of the compactor´s lifecycle performances are linked to a Net Present Value (NPV) model and a sustainability assessment. The model is then further explored and evaluated in the Decision Arena, located at Blekinge Institute of Technology.  The simulated model is created to approach a ‘lifelike’ lifecycle of the machine, containing the compactor´s ordinary usage in road construction. This includes operations in sidewalk, parking lot and pothole repair scenarios. The model contain service, maintenance, transport, workers, resource sharing and more. The model is connected to MS Excel to transfer data. The life cycle performances are captured in the model and used to estimate the cost parameters of energy -, water -, maintenance -, service - and transportation energy cost within the NPV model. The CO2 – emission for fuel consumption and transport, together with the total water consumption in the sustainability assessment.  The outcome of the thesis showed that the method gave good results for developing new design configurations in the early phases in product development. The method could support designing towards sustainable and long-term solutions and collaborations over the sectors (i.e. between stakeholders, engineers, designers, non-experts and more). The outcome in the specific case resulted in successfulness of capturing all lifecycle performances of the machine and linking them to the mentioned parameters. The research question is, however, generic and the investigation for the specific case study uses assumptions and up- and down scaled data to protect the company secrecy. For future work, the method together with Internet of Things (IoT), Digital Twin or Industry 4.0 could be in high interest to investigate further. / Detta examensarbete har blivit utfört i association med Blekinge Tekniska högskolan och i samarbete med företaget Dynapac Compaction Equipment AB. Syftet med projektet är att undersöka hur diskret händelsesimulering (DES) kan användas för värde - och hållbarhets bedömning för olika designkonfigurationer, i tidiga skeden av produktutvecklingen. Arbetet är utfört genom att tillämpa exemplet av att simulera livscykeln för en asfaltsvält med dubbla trummor. Simuleringsmodellen är framställd genom det databaserade DES programmet Simio LLC, där utdata för maskinens livscykelprestanda tas fram och kopplas till en Net Present Value (NPV) modell och en hållbarhetsdömning för maskinen. Simuleringsmodellen utforskas och bedöms sedan vidare i ’Decision Arena’ på Blekinge Tekniska Högskola.  Den simulerade modellen är framställd för att eftersträva en verklighetstrogen livscykel av maskinen, innehållande dess vanliga användningsområden inom vägarbete. I livscykeln inkluderas operationer av trottoarer, parkeringsplatser och reparationer av hål i vägbanor. Modellen innehåller även service och underhåll, transport, arbetare/anställda, resursdelning med mera. Modellen är kopplad till MS Excel för att föra över in- och utdata mellan programmen. Maskinens livscykelprestanda är hämtat från modellen och använt till att uppskatta kostnadsparametrarna för energi, vatten, underhåll, service och energi under transport i NPV – modellen. Maskinens CO2 – utsläpp för bränsleförbrukning och transport, tillsammans med vattenkonsumtionen i hållbarhetsbedömningen. Arbetet visar på goda resultat för att utveckla nya desginkonfigurationer i de tidiga skedena inom produktutveckling. Metoden kan stödja utformning mot hållbara och långsiktiga lösningar, samt förstärka samarbeten över sektorerna (dvs. mellan intressenter, ingenjörer, designers, icke-experter med mera). Utfallet för det specifika fallet resulterade i framgång med att fånga upp maskinens livscykelprestanda och koppla dessa till de ovan nämnda parameterana. Forskningsfrågan är dock generell och utredningen för den specifika fallstudien använder uppskattningar och upp- och nerskalade data för att skydda företagets sekretess. För framtida arbete, kan metoden tillsammans med Internet of Things (IoT), Digital Twin och Industry 4.0 vara av stort intresse för att undersöka.

Based on the generating matrix to the Tribonacci sequence, the Tribonacci cat map is a discrete chaotic dynamical system, similar to Arnold's discrete cat map, but on three dimensional space. In this thesis, this new mapping is introduced and the properties of its matrix are presented. The main results of the investigation prove how the size of the domain of the map affects its period and explore the orbit lengths of non-trivial points. Different upper bounds to the map are studied and proved, and a conjecture based on numerical calculations is proposed. The Tribonacci cat map is used for applications such as 3D image encryption and colour encryption. In the latter case, the results provided by the mapping are compared to those from a generalised form of the map.