As more and more wireless applications/services emerge in the market, the already heavily crowded radio spectrum becomes much scarcer. Meanwhile, however,as it is reported in the recent literature, there is a large amount of radio spectrum that is under-utilized. This motivates the concept of cognitive radio wireless networks that allow the unlicensed secondary-users (SUs) to dynamically use the vacant radio spectrum which is not being used by the licensed primary-users (PUs). In this dissertation, we investigate protocol design for both the synchronous and asynchronous cognitive radio networks with emphasis on the medium access control (MAC) layer. We propose various spectrum sharing schemes, opportunistic packet scheduling schemes, and spectrum sensing schemes in the MAC and physical (PHY) layers for different types of cognitive radio networks, allowing the SUs to opportunistically utilize the licensed spectrum while confining the level of interference to the range the PUs can tolerate. First, we propose the cross-layer based multi-channel MAC protocol, which integrates the cooperative spectrum sensing at PHY layer and the interweave-based spectrum access at MAC layer, for the synchronous cognitive radio networks. Second, we propose the channel-hopping based single-transceiver MAC protocol for the hardware-constrained synchronous cognitive radio networks, under which the SUs can identify and exploit the vacant channels by dynamically switching across the licensed channels with their distinct channel-hopping sequences. Third, we propose the opportunistic multi-channel MAC protocol with the two-threshold sequential spectrum sensing algorithm for asynchronous cognitive radio networks. Fourth, by combining the interweave and underlay spectrum sharing modes, we propose the adaptive spectrum sharing scheme for code division multiple access (CDMA) based cognitive MAC in the uplink communications over the asynchronous cognitive radio networks, where the PUs may have different types of channel usage patterns. Finally, we develop a packet scheduling scheme for the PU MAC protocol in the context of time division multiple access (TDMA)-based cognitive radio wireless networks, which is designed to operate friendly towards the SUs in terms of the vacant-channel probability. We also develop various analytical models, including the Markov chain models, M=GY =1 queuing models, cross-layer optimization models, etc., to rigorously analyze the performance of our proposed MAC protocols in terms of aggregate throughput, access delay, and packet drop rate for both the saturation network case and non-saturation network case. In addition, we conducted extensive simulations to validate our analytical models and evaluate our proposed MAC protocols/schemes. Both the numerical and simulation results show that our proposed MAC protocols/schemes can significantly improve the spectrum utilization efficiency of wireless networks.

No description available.

Técnicas de gerenciamento de filas e descarte de pacotes são empregadas pelos escalonadores de pacotes presentes nos roteadores internos de uma rede de telecomunicações. Devido às características auto-similares do tráfego presente nas redes, o desenvolvimento de modelos para análise de desempenho de protocolos e de elementos de rede é enormemente dificultado. Tais características auto-similares são oriundas da ação dos protocolos predominantes nas redes em questão, e dos mecanismos fim-a-fim de controle de congestionamento existentes, determinantes no comportamento do fluxo de informações entre diferentes camadas na hierarquia de protocolos TCP/IP. Esta tese tem como objetivo principal propor modelos analíticos de baixo esforço computacional que permitam fazer uma análise de desempenho de um nó de rede (podendo este nó ser do tipo: DiffServ, IntServ, IP, Multi Protocol Label Switching, entre outros) com o escalonador WFQ. O tráfego considerado é do tipo TCP, devido ao fato que este protocolo é o mais utilizado na Internet atualmente, apresentando, portanto, características auto-similares. Foram desenvolvidos modelos para o escalonador WFQ quando o mesmo é alimentado com tráfego Poissoniano e tráfego do tipo auto-similar. O primeiro modelo está baseado em uma cadeia de Markov bidimensional para representar o comportamento do escalonador WFQ alimentado por dois fluxos de prioridades diferentes. O segundo modelo faz uso de duas filas separadas com taxas de serviço ajustadas de modo a simular o comportamento do escalonador WFQ. As filas são do tipo M[X]/M/1/B para levar em conta o comportamento auto-similar do tráfego. Como resultado, mostra-se que o segundo modelo é capaz de estimar as métricas de desempenho, com erro aceitável, dentro de uma faixa adequada de valores dos parâmetros do sistema, conforme demonstra a validação de resultados conduzido com uso do software NS-2. / Internal routers of telecommunication networks employ a variety of queue management and packet discarding techniques. The development of models for analyzing performance of different protocols and devices is made difficult by the self-similar nature of network traffic. Traffic self-similarity stems from the action of predominant protocols and end-to-end congestion control systems, which are key factors in determining the behavior of data flow between layers of the TCP/IP protocol stack. This thesis proposes analytical models that allow for the evaluation of a (DiffServ, IntServ, IP, Multi Protocol Label Switching etc.) network node's performance at a low computational cost. Only TCP traffic is considered, since it accounts for most of current Internet traffic and therefore exhibits self-similar characteristics. Models were developed for the WFQ scheduler with Poisson and self-similar traffic inputs. The former is based on a bi-dimensional Markov chain representing the behavior of the WFQ scheduler with two input flows with different priorities. The latter consists in two separate queues whose service rates are tuned so as to simulate the behavior of a WFQ scheduler. M[X]/M/1/B queues are used to account for the self-similar nature of traffic. As a result, it is shown that the second model accurately estimates performance metrics for certain ranges of parameter values, as confirmed by NS-2 simulations.

Orientador: Renato Baldini Filho / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-05T14:02:39Z (GMT). No. of bitstreams: 1 Oliveira_CarlosHenriqueRodriguesde_D.pdf: 6124095 bytes, checksum: d981e4a9e163dc0b358b20c451c92109 (MD5) Previous issue date: 2005 / Resumo: Este trabalho de tese estuda e analisa o desempenho dos sistemas móveis celulares GSM de segunda geração (2G), GPRS de segunda geração intermediária (2,5G) e CDMA2000 de terceira geração (3G). Na primeira parte deste trabalho de tese são avaliadas estratégias de compartilhamento dos canais de comunicação utilizados pelos sistemas GSM e GPRS, em busca daquela que resulte no menor impacto na qualidade dos serviços prestados por ambas as redes. Para esta avaliação, e como contribuição deste trabalho de tese, são desenvolvidos algoritmos aplicados em um simulador de eventos discretos desenvolvido em linguagem de programação C/C++. Os resultados das simulações mostram que a reserva de canais exclusivos ao sistema GPRS apresenta degradação na qualidade de serviço prestado pelo sistema GSM e que a melhor estratégia de compartilhamento é utilizar os canais de comunicação para o sistema GPRS nos momentos em que estes canais não são usados pelo sistema GSM. Na segunda parte deste trabalho de tese são feitas análises de desempenho dos sistemas móveis celulares de terceira geração, CDMA2000 lxRTT e CDMA2000 lxEVDO, baseadas na qualidade do serviço prestado por estas redes operando com várias aplicações simultâneas fim-a-fim entre cliente e servidor. Técnicas de detecção multiusuário e de antenas adaptativas são utilizadas na recepção destas aplicações e é avaliada a nova qualidade de serviço. Para estas análises de desempenho e como contribuição deste trabalho de tese, modelos de simulação são desenvolvidos utilizando a ferramenta OPNET. As redes CDMA2000 lxRTT e lxEVDO apresentam bom desempenho, analisado pelo parâmetro atraso da qualidade de serviço, na passagem de tráfego das aplicações HTTP, E-mail, VoIP, FTP, Telnet e Acesso a Banco de Dados. O desempenho da rede CDMA2000 lxEVDO melhora tanto com detecção multiusuário como com antenas adaptativas em relação ao receptor rake / Abstract: This thesis work studies and analyzes the performance of cellular mobile systems GSM of second generation (2G), GPRS of second intermediate generation (2,5G) and CDMA2000 of third generation (3G). In the first part of this thesis work, sharing strategies of communication channels used by GSM and GPRS systems are evaluated to find the one that results in the lowest impact in the quality of services supported by both networks. To this evaluation, and as contribution of this thesis work, algorithms applied in a discrete-event simulator developed in C/C++ programming language are developed. The simulation results show that the reserve of exclusive channels to the GPRS system presents degradation in the quality of service given for GSM system and that the better sharing strategy is to use the communication channels for the GPRS system whenever these channels are not used by the GSM system. In the second part of this thesis work, performance analyses of the third generation cellular mobile systems, CDMA2000 lxRTT and CDMA2000 lxEVDO, based on the quality of service supported by these networks operating with several end-to-end simultaneous applications between client and server are made. Multiuser detection and adaptive antennas techniques are used in the reception of these applications and the new quality of service is evaluated. For these performance analyses, and as contribution of this thesis work, simulation models are developed using the OPNET tool. The CDMA2000 lxRTT and lxEVDO networks present good performance analyzed through the delay parameter of quality of service running HTTP, E-mail, VolP, FTP, Telnet and Data Base Access applications. The CDMA2000 lxEVDO network performance improves using either multiuser detection or adaptive antennas when compared with rake receiver / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Le problème de dimensionnement et planification d'agents en centre d'appels consiste à déterminer sur une période le nombre d'interlocuteurs requis afin d'atteindre la qualité de service exigée et minimiser les coûts induits. Ce sujet fait l'objet d'un intérêt croissant pour son intérêt théorique mais aussi pour l'impact applicatif qu'il peut avoir. Le but de cette thèse est d'établir des approches en contraintes en probabilités en considérant l'incertitude de la demande.Tout d'abord, la thèse présente un modèle en problème d'optimisation stochastique avec contrainte en probabilité jointe traitant la problématique complète en une étape afin d'obtenir un programme facile à résoudre. Une approche basée sur l'idée de continuité est proposée grâce à des lois de probabilité continues, une nouvelle relation entre les taux d'arrivées et les besoins théoriques et la linéarisation de contraintes. La répartition du risque global est faite pendant le processus d'optimisation, permettant une solution au coût réduit. Ces solutions résultantes respectent le niveau de risque tout en diminuant le coût par rapport à d'autres approches.De plus, le modèle en une étape est étendu pour améliorer sa représentation de la réalité. D'une part, le modèle de file d'attente est amélioré et inclus la patience limitée des clients. D'autre part, une nouvelle expression de l'incertitude est proposée pour prendre la dépendance des périodes en compte.Enfin, une nouvelle représentation de l'incertitude est considérée. L'approche distributionally robust permet de modéliser le problème sous l'hypothèse que la loi de probabilité adéquate est inconnue et fait partie d'un ensemble de lois, défini par une moyenne et une variance données. Le problème est modélisé par une contrainte en probabilité jointe. Le risque à chaque période est définie par une variable à optimiser.Un problème déterministe équivalent est proposé et des approximations linéaires permettent d'obtenir une formulation d'optimisation linéaire. / The staffing and shift-scheduling problems in call centers consist in deciding how many agents handling the calls should be assigned to work during a given period in order to reach the required Quality of Service and minimize the costs. These problems are subject to a growing interest, both for their interesting theoritical formulation and their possible applicative effects. This thesis aims at proposing chance-constrained approaches considering uncertainty on demand forecasts.First, this thesis proposes a model solving the problems in one step through a joint chance-constrained stochastic program, providing a cost-reducing solution. A continuous-based approach leading to an easily-tractable optimization program is formulated with random variables following continuous distributions, a new continuous relation between arrival rates and theoritical real agent numbers and constraint linearizations. The global risk level is dynamically shared among the periods during the optimization process, providing reduced-cost solution. The resulting solutions respect the targeted risk level while reducing the cost compared to other approaches.Moreover, this model is extended so that it provides a better representation of real situations. First, the queuing system model is improved and consider the limited patience of customers. Second, another formulation of uncertainty is proposed so that the period correlation is considered.Finally, another uncertainty representation is proposed. The distributionally robust approach provides a formulation while assuming that the correct probability distribution is unknown and belongs to a set of possible distributions defined by given mean and variance. The problem is formulated with a joint chance constraint. The risk at each period is a decision variable to be optimized. A deterministic equivalent problem is proposed. An easily-tractable mixed-integer linear formulation is obtained through piecewise linearizations.

L'un des challenges le plus important pour les opérateurs des réseaux mobiles est de dimensionner le réseau de la manière la plus efficace possible, c'est-à-dire, bien planifier les ressources pour fournir une bonne couverture et une meilleure capacité. Afin de mieux gérer le trafic généré dans le réseau, les opérateurs déploient des petites cellules pour aider les macro-cellules à délester les zones de la cellule où le trafic de données est significativement supérieur au trafic moyen dans la cellule. Cependant, le problème majeur de ces réseaux hétérogènes consiste à bien localiser ces hotspots et puis de mettre en place la meilleure solution pour les absorber. Dans cette thèse, on traite le sujet de localisation de hotspot et on étudie l'impact de son imperfection sur les performances des déploiements des réseaux hétérogènes. Dans une première étape, on propose une nouvelle méthode de localisation de hotspot. Puis, on propose d'évaluer l'impact d'une mauvaise localisation de trafic sur le déploiement des petites cellules à travers une analyse de performances au niveau statique et dynamique. Sachant qu'une grande quantité de trafic de données dans le réseau mobile est générée par des utilisateurs qui sont en mouvement, on propose d'évaluer les performances des petites cellules mobiles. Enfin, la quatrième étape consiste à améliorer encore la solution de déploiement de petites cellules en utilisant les drones. On propose un mécanisme de décongestion du réseau et on discute les avantages et les points à explorer. Une analyse de performance est aussi réalisée pour comparer cette solution avec les solutions classiques de macro cellules et de petites cellules / The continuous increasing traffic in cellular networks has forced the mobile operators to look for efficient and viable options to manage their networks so as to ensure more efficiency over the network life cycle while also evolving with the implementation of new technologies. Traffic hotspot localization can help operators to identify the areas where deploying small cells can reduce the congestion. We firstly propose and assess a new traffic hotspot localization method based on the projection of O&M KPIs on the coverage map. Compared to probing methods, the computational costs and the equipment expenditures are reduced. Moreover, the localization accuracy is improved. Next, in order to evaluate the impact of the limited accuracy of traffic localization tools on small cell deployment, we study the performances of three different scenarios. The first one considers a network of macrocells only and represents a benchmark to decide about the usefulness of small cells. The second one is based on a network of macrocells with a perfectly deployed small cell allowing to identify the limitations of small cell deployment and the last one is with an imperfectly deployed small cell. Realizing that a significant amount of cellular demand is generated on the go and suffers deteriorating quality, we investigate the potential performance gains of using moving small cells. The major outcome is to understand if moving cells leverage the relative operators' investments. Finally, we propose a new mobile data offloading mechanism which capitalizes on drone small cells to alleviate the data traffic load. We realize a performance evaluation and comparison with classic small cell deployment

Nous étudions des modèles mathématiques issus de la théorie des files d’attente pour évaluer et optimiser les performances des mécanismes de partage de ressources entre flots dans les réseaux. Dans une première partie, nous proposons des approximations simples et explicites des principales métriques de performance des flots élastiques dans les réseaux à partage de bande passante opérant sous le mode ”équité équilibré”. Nous étudions ensuite le partage de bande passante entre flux élastiques et flux de streaming en supposant que le nombre de ces derniers est limité par un mécanisme de contrôle d’admission et proposons des approximations de performance basées sur une hypothèse de quasi stationnarité. Les résultats de simulation montrent le bon niveau de précision des approximations proposées.Dans une deuxième partie, nous étudions le compromis entre délai et énergie dans les réseaux à partage de bande passante dont les noeuds peuvent réguler leur vitesse en fonction de la charge du système. En supposant que le réseau est initialement dans un état de congestion, on s’intéresse à la politique optimale d’allocation de débit permettant de le vider à coût minimal. L’analyse de la politique stochastique optimale via la théorie des processus de décision markoviens étant extrêmement difficile, nous proposons de l’approximer en utilisant un modèle fluide déterministe qui peut être résolu grâce à des techniques de contrôle optimal. Pour le cas d’un seul lien partagé par plusieurs classes de trafic, on montre que la politique optimale correspond à la règle cμ et on propose une expression explicite de la vitesse optimale. Enfin, dans une troisième partie, on s’intéresse aux plateformes de Cloud Computing dans le cadre du modèle SaaS. En supposant un partage équitable des ressources physiques entre machines virtuelles s’exécutant de manière concurrente, nous proposons des modèles de file d’attente simples pour prédire les temps de réponse des applications. Les modèles proposés prennent explicitement en compte le comportement des différentes classes d’application (tâches interactives, de calcul ou permanentes). Les expérimentations menées sur une plateforme réelle montrent que les modèles mathématiques obtenus permettent de prédire les temps de réponse avec une bonne précision. / We study queueing-theoretic models for the performance evaluation and optimization of bandwidth-sharing networks. We first propose simple and explicit approximations for the main performance metrics of elastic flows in bandwidth-sharing networks operating under balanced fairness. Assuming that an admission control mechanism is used to limit the number of simultaneous streaming flows, we then study the competition for bandwidth between elastic and streaming flows and propose performance approximations based on a quasi-stationary assumption. Simulation results show the good accuracy of the proposed approximations. We then investigate the energy-delay tradeoff in bandwidth-sharing networks in which nodes can regulate their speed according to the load of the system. Assuming that the network is initially congested, we investigate the rate allocation to the classes that drains out the network with minimum total energy and delay cost. We formulate this optimal resource allocation problem as a Markov decision process which proves tobe both analytically and computationally challenging. We thus propose to solve this stochastic problem using a deterministic fluid approximation. For a single link sharedby an arbitrary number of classes, we show that the optimal-fluid solution follows thewell-known cμ rule and give an explicit expression for the optimal speed. Finally, we consider cloud computing platforms under the SaaS model. Assuming a fair share of the capacity of physical resources between virtual machines executed concurrently, we propose simple queueing models for predicting response times of applications.The proposed models explicitly take into account the different behaviors of the different classes of applications (interactive, CPU-intensive or permanent applications). Experiments on a real virtualized platform show that the mathematical models allow to predict response times accurately

Serverless edge computing is a distributed network and computing system in which the data is processed at the edge of the network based on serverless architecture. It can provide large-scale computing and storage resources with low latency, which are very useful in AI applications such as object detection. However, when analyzing serverless computing architectures, we model them using simple models, such as single server or multi-server queues, and it is important to make sure these models can explain the behaviors of real systems. Therefore, we focus on the performance evaluation of serverless edge computing for AI applications in this project. With that, we aim at proposing more realistic and accurate models for real serverless architectures. In this project, our objective is to evaluate the performance and model mathematically an object-detection application running on a serverless architecture implemented with Kubernetes. This project provides a detailed description of the implementation of the serverless platform and YOLOv5-based object detection application. After implementation, we design experiments and make performance evaluations of the time of object detection results and quality of object detection results. Finally, we conclude that the number of users in the system significantly affects the service time. We observe that there is no queue in the system, so we cannot just use mathematical models with a queue to model the system. Therefore, we consider that the processor sharing model is more appropriate for modeling this serverless architecture. This is very helpful for giving insights on how to make more realistic and accurate mathematical queueing models for serverless architectures. For future work, other researchers can also implement our serverless platform and do further development, such as deploying other serverless applications on it and making performance evaluations. They can also design other use-cases for the experiments and make further analyses on queue modeling of serverless architecture based on this project. / Serverless edge computing är ett distribuerat nätverk och datorsystem där data bearbetas i kanten av nätverket baserat på serverlös arkitektur. Det kan tillhandahålla storskaliga dator- och lagringsresurser med låg latens, vilket är mycket användbart i AI-applikationer som objektdetektering. Men när vi analyserar serverlösa datorarkitekturer modellerar vi dem med hjälp av enkla modeller, till exempel enstaka servrar eller köer med flera servrar, och det är viktigt att se till att dessa modeller kan förklara beteendet hos verkliga system. Därför fokuserar vi på prestandautvärdering av serverlös edge computing för AI-applikationer i detta projekt. Med det siktar vi på att föreslå mer realistiska och exakta modeller för riktiga serverlösa arkitekturer. I detta projekt är vårt mål att utvärdera prestandan och matematiskt modellera en objektdetekteringsapplikation som körs på en serverlös arkitektur implementerad med Kubernetes. Detta projekt ger en detaljerad beskrivning av implementeringen av den serverlösa plattformen och den YOLOv5-baserade objektdetekteringsapplikationen. Efter implementering designar vi experiment och gör prestandautvärderingar av tidpunkten för objektdetekteringsresultat och kvaliteten på objektdetekteringsresultaten. Slutligen drar vi slutsatsen att antalet användare i systemet avsevärt påverkar servicetiden. Vi observerar att det inte finns någon kö i systemet, så vi kan inte bara använda matematiska modeller med en kö för att modellera systemet. Därför anser vi att processordelningsmodellen är mer lämplig för att modellera denna serverlösa arkitektur. Detta är mycket användbart för att ge insikter om hur man gör mer realistiska och exakta matematiska kömodeller för serverlösa arkitekturer. För framtida arbete kan andra forskare också implementera vår serverlösa plattform och göra vidareutveckling, såsom att distribuera andra serverlösa applikationer på den och göra prestandautvärderingar. De kan även designa andra användningsfall för experimenten och göra ytterligare analyser av kömodellering av serverlös arkitektur utifrån detta projekt.

Accounting for some the highest arrival rates and widest varieties of medical conditions in a hospital, the emergency department is highly dependent on efficient operations strategies in order to function effectively and provide qualitative health care. This is especially true for the emergency department of Karolinska University Hospital in Huddinge from which real patient data has been obtained. In attempting to improve service levels, current operational structures are evaluated and several different scenarios are simulated mathematically in this study. After validating the adequacy of modeling the emergency department as a Jackson Network, the network is simulated for various combinations of patient flow parameters enabling the study of the effects of resource allocation strategies. The results indicate that the current organization of, and resources available to, the emergency department leaves room for improvement in terms of service levels. Resource levels needed for specific target levels of service are found and the optimal allocations of resources is discussed. Additionally, a brief literature review of operations strategies and how simulation tools can serve as decision support systems for operations strategy managers is conducted. / Akutmottagningen är en av de avdelningar på ett sjukhus som utsätts för högst ankomstintensiteter och bredast variationer av besöksorsaker vilket orsakar höga krav på att utveckla effektiva verksamhetsstrategier för att upprätthålla en kvalitativ sjukvård. Akutmottagningen på Karolinska Universitetssjukhuset i Huddinge har studerats genom patientdata. För att försöka förbättra servicenivåer och förkorta väntetider för patienter utvärderas verksamhetens organisation och struktur. En matematisk modell av verksamhetens organisation konstrueras och valideras, varefter effekterna av olika resursallokeringar analyseras genom matematiska simuleringar. Resultaten visar på att akutvården som den är organiserad idag lämnar utrymme för förbättring och optimering av resursallokering. Genom matematiska simuleringar identifieras marginella resursers specifika servicenivåer och relativa förändringar i servicenivåer. Slutligen kompletteras den matematiska analysen med en kortare litteraturstudie. Här presenteras hur simuleringar kan utgöra beslutsstödsystem för att planera resursallokering och introducera lean-strategier i sjukvården.

Åre ski resort is the largest and most renowned ski resort in Sweden, offering excellent skiing opportunities, restaurants, and nightlife in a prime location. Meanwhile, it is often subject to heavy traffic during the peak season and has earned a bad reputation for struggling with long lift queues. To address the issue, this paper aimed at analyzing the current capacity of the ski resort with the purpose of identifying areas and cost-efficient measures for improvement. It was done by modeling the ski system as a Jackson Network based on queuing theory, with relevant parameters extracted from actual skier data provided by the operating company Skistar. Several models were constructed to capture varying skiing patterns throughout the day and under different weather conditions. The models suggested that the lift queues first start to form at the lifts VM 8:an, Sadelexpressen, and Bräckeliften when the number of skiers in the system ranges from 3,700 to 6,200. Recommendations were then proposed to Skistar on how to resolve the identified bottlenecks and increase the resort’s capacity to a range of 6,000 to 8,400 skiers. Lastly, the models estimated that the resort could / Åre är en av Sveriges mest populära skidorter, som med utmärkta kommunikationsmöjligheter erbjuder fantastisk skidåkning och ett brett utbud av restauranger och nöjesliv. Skidsystemet belastas samtidigt hårt under högsäsong och har ådragit sig ett rykte om att ofta vara drabbat av långa liftköer. Mot bakgrund av detta ämnade denna rapport att analysera skidsystemets kapacitet och identifiera förbättringsområden för att ta itu med problemet. Analysen grundade sig i en modellering av skidsystemet, utformat som ett Jacksonnätverk i enlighet med köteori. Skistar, som ansvarar för driften av skidsystemet, tillhandahöll data som låg till grund för framtagandet av nätverkets parametrar. Genom jämförelser mellan olika modeller kunde dagliga förändringar i åkmönster och variationer under olika väderförhållanden tas i beaktning i analysen. Modellerna indikerade att liftarna VM 8:an, Sadelexpressen och Bräckeliften först drabbas av köbildning, vilket sker då antalet skidåkare i systemet är mellan 3 700 och 6 200. De identifierade flaskhalsarna låg till grund för de rekommendationer som formulerades till Skistar och som innehöll kostnadseffektiva förslag på förändringar. Dessa skulle förbättra kapaciteten till en nivå mellan 6 000 och 8 400 skidåkare. Till sist estimerade modellerna systemets maximala kapacitet till 14 000 skidåkare, vilket endast uppnås vid ett optimalt nyttjande av samtliga liftar.