Thesis (Ph.D.)--McMaster University, 2004. / Advisor: George Steiner. Includes bibliographical references (leaves 87-91). Also available via World Wide Web.

Deregulation of electricity markets, increased usage of intermittent energy sources, and growing environmental concerns have created a volatile process manufacturing environment. Survival under this new paradigm requires chemical manufactures to shift from the traditional steady-state operation to a more dynamic and flexible operation mode. Under more frequent operating changes, the transition dynamics become increasingly relevant, rendering the traditional steady-state based scheduling decision-making suboptimal. This has motivated calls for the integration of scheduling and control. In an integrated scheduling and control framework, the scheduling decisions are based on a dynamic representation of the process. While various integration paradigms are proposed in the literature, our study concentrates on the closed-loop integration of scheduling and control. There are two main advantages to this approach: (i) seamless integration with the existing control system (i.e. it does not require a new control system infrastructure), (ii) the framework is aware of the control system dynamics, and hence has knowledge of the closed-loop process dynamics. The later aspect is particularly important as the control system plays a key role in determining the transition dynamics. The first part of our work is dedicated to developing an integrated scheduling and control framework that computes set-point trajectories, to be tracked by the lower-level linear model predictive control system, that are robust to demand uncertainty. We employ a piecewise linear representation of the nonlinear process model to obtain a mixed-integer linear programming (MILP) problem, thus alleviating the computational complexity compared to a mixed-integer nonlinear programming formulation. The value of the stochastic solution is used to confirm the superiority of the robust formulation against a nominal one that disregards uncertainty. In the second part of this study, we expand the framework to accommodate additional uncertainty types, including model and cost uncertainty. In the third part of this thesis, a deterministic integrated scheduling and control framework for processes controlled by distributed linear model predictive control is developed. The integrated problem is formulated as a MILP. To reduce the solution time, we introduce strategies to approximate the feedback control action. Through case studies, we demonstrate that knowledge of the control system enables the framework to effectively coordinate the MPC subsystems. The framework performs well even under conditions of plant-model mismatch conditions. In the final part of this study, we introduce an integrated scheduling and control formulation for processes controlled by nonlinear model predictive control (NMPC). Here, discrete scheduling decisions are represented using complementarity conditions. Additionally, we use the first-order Karush-Kuhn-Tucker conditions of the NMPC controller to compute the input values in the integrated problem. The resulting problem is a mathematical program with complementarity constraints that we solve using a regularization approach. For all case studies, the complementarity formulation effectively capture discrete scheduling decisions, and the KKT conditions always provides a local optimum of the associated NMPC problem. In summary, this study of the integration of scheduling and control addresses various control systems, uncertainty, and strategies for enhancing the solution time. Furthermore, we assess the performance of the proposed frameworks under conditions of plant-model mismatch, a common scenario in real-life applications. / Thesis / Doctor of Philosophy (PhD)

Production planning problems are of paramount importance within supply chain planning, supporting decisions on the transformation of raw materials into finished products. Lot sizing in production planning refers to the tactical/operational decisions related to the size and timing of production orders to satisfy a demand. The objectives of lot-sizing problems are generally economical-related, such as saving costs or increasing profits, though other aspects may be taken into account such as quality of the customer service and reduction of inventory levels. Lot-sizing problems are very common in production activities and an efficient planning of such activities gives the company a clear advantage over concurrent organizations. To that end it is required the consideration of realistic features of the industrial environment and product characteristics. By means of mathematical modelling, such considerations are crucial, though their inclusion results in more complex formulations. Although lot-sizing problems are well-known and largely studied, there is a lack of research in some real-world aspects. This thesis addresses two main characteristics at the lot-sizing context: (a) setup crossover; and (b) perishable products. The former allows the setup state of production line to be carried over between consecutive periods, even if the line is not yet ready for processing production orders. The latter characteristic considers that some products have fixed shelf-life and may spoil within the planning horizon, which clearly affects the production planning. Furthermore, two types of perishable products are considered, according to the duration of their lifetime: medium-term and short-term shelf-lives. The latter case is tighter than the former, implying more constrained production plans, even requiring an integration with other supply chain processes such as distribution planning. Research on stronger mathematical formulations and solution approaches for lot-sizing problems provides valuable tools for production planners. This thesis focuses on the development of mixed-integer linear programming (MILP) formulations for the lot-sizing problems considering the aforementioned features. Novel modelling techniques are introduced, such as the proposal of a disaggregated setup variable and the consideration of lot-sizing instead of batching decisions in the joint production and distribution planning problem. These formulations are subjected to computational experiments in state-of-the-art MILP-solvers. However, the inherent complexity of these problems may require problemdriven solution approaches. In this thesis, heuristic, metaheuristic and matheuristic (hybrid exact and heuristic) procedures are proposed. A lagrangean heuristic addresses the capacitated lot-sizing problem with setup carryover and perishable products. A novel dynamic programming procedure is used to achieve the optimal solution of the uncapacitated single-item lot-sizing problem with setup carryover and perishable item. A heuristic, a fix-and-optimize procedure and an adaptive large neighbourhood search approach are proposed for the operational integrated production and distribution planning. Computational results on generated set of instances based on the literature show that the proposed methods yields competitive performances against other literature approaches. / Problemas de planejamento da produção são de suma importância no planejamento da cadeia de suprimentos, dando suporte às decisões da transformação de matérias-primas em produtos acabados. O dimensionamento de lotes em planejamento de produção é definido pelas decisões tático-operacionais relacionadas com o tamanho das ordens de produção e quando fabricá-las para satisfazer a demanda. Os objetivos destes problemas são geralmente de cunho econômico, tais como a redução de custos ou o aumento de lucros, embora outros aspectos possam ser considerados, tais como a qualidade do serviço ao cliente e a redução dos níveis de estoque. Problemas de dimensionamento de lotes são muito comuns em atividades de produção e um planejamento eficaz de tais atividades, estabelece uma clara vantagem à empresa em relação à concorrência. Para este objetivo, é necessária a consideração de características realistas do ambiente industrial e do produto. Para a modelagem matemática do problema, estas considerações são cruciais, embora sua inclusão resulte em formulações mais complexas. Embora os problemas de dimensionamento de lotes sejam bem conhecidos e amplamente estudados, várias características reais importantes não foram estudadas. Esta tese aborda, no contexto de dimensionamento de lotes, duas características muito relevantes: (a) preservação da preparação total e parcial; e (b) produtos perecíveis. A primeira permite que o estado de preparação de uma linha de produção seja mantido entre dois períodos consecutivos, mesmo que a linha de produção ainda não esteja totalmente pronta para o processamento de ordens de produção. A ultima característica determina que alguns produtos tem prazo de validade fixo, menor ou igual do que o horizonte de planejamento, o que afeta o planejamento da produção. Além disso, de acordo com a duração de sua vida útil, foram considerados dois tipos de produtos perecíveis: produtos com tempo de vida de médio e curto prazo. O ultimo caso resulta em um problema mais apertado do que o anterior, o que implica em planos de produção mais restritos. Isto pode exigir uma integração com outros processos da cadeia de suprimentos, tais como o planejamento de distribuição dos produtos acabados. Pesquisas sobre formulações matemáticas mais fortes e abordagens de solução para problemas de dimensionamento de lotes fornecem ferramentas valiosas para os planejadores de produção. O foco da tese reside no desenvolvimento de formulações de programação linear inteiro-mistas (MILP) para os problemas de dimensionamento de lotes, considerando as características mencionadas anteriormente. Novas técnicas de modelagem foram introduzidas, como a proposta de variáveis de preparação desagregadas e a consideração de decisões de dimensionamento de lotes ao invés de decisões de agrupamento de ordens de produção no problema integrado de planejamento de produção e distribuição. Estas formulações foram submetidas a experimentos computacionais em MILP-solvers de ponta. No entanto, a complexidade inerente destes problemas pode exigir abordagens de solução orientadas ao problema. Nesta tese, abordagens heurísticas, metaheurísticas e matheurísticas (híbrido de métodos exatos e heurísticos) foram propostas para os problemas discutidos. Uma heurística lagrangeana aborda o problema de dimensionamento de lotes com restrições de capacidade, preservação da preparação total e produtos perecíveis. Um novo procedimento de programação dinâmica e utilizado para encontrar a solução ótima do problema de dimensionamento de lotes de um único produto perecível, sem restrições de capacidade e preservação da preparação total. Uma heurística, um procedimento x-and-optimize e uma abordagem por buscas adaptativas em grande vizinhanças são propostas para o problema integrado de planejamento de produção e distribuição. Resultados computacionais em conjuntos de instâncias geradas com base na literatura mostram que os métodos propostos obtiveram performances competitivas com relação a outras abordagens da literatura.

Production planning problems are of paramount importance within supply chain planning, supporting decisions on the transformation of raw materials into finished products. Lot sizing in production planning refers to the tactical/operational decisions related to the size and timing of production orders to satisfy a demand. The objectives of lot-sizing problems are generally economical-related, such as saving costs or increasing profits, though other aspects may be taken into account such as quality of the customer service and reduction of inventory levels. Lot-sizing problems are very common in production activities and an efficient planning of such activities gives the company a clear advantage over concurrent organizations. To that end it is required the consideration of realistic features of the industrial environment and product characteristics. By means of mathematical modelling, such considerations are crucial, though their inclusion results in more complex formulations. Although lot-sizing problems are well-known and largely studied, there is a lack of research in some real-world aspects. This thesis addresses two main characteristics at the lot-sizing context: (a) setup crossover; and (b) perishable products. The former allows the setup state of production line to be carried over between consecutive periods, even if the line is not yet ready for processing production orders. The latter characteristic considers that some products have fixed shelf-life and may spoil within the planning horizon, which clearly affects the production planning. Furthermore, two types of perishable products are considered, according to the duration of their lifetime: medium-term and short-term shelf-lives. The latter case is tighter than the former, implying more constrained production plans, even requiring an integration with other supply chain processes such as distribution planning. Research on stronger mathematical formulations and solution approaches for lot-sizing problems provides valuable tools for production planners. This thesis focuses on the development of mixed-integer linear programming (MILP) formulations for the lot-sizing problems considering the aforementioned features. Novel modelling techniques are introduced, such as the proposal of a disaggregated setup variable and the consideration of lot-sizing instead of batching decisions in the joint production and distribution planning problem. These formulations are subjected to computational experiments in state-of-the-art MILP-solvers. However, the inherent complexity of these problems may require problemdriven solution approaches. In this thesis, heuristic, metaheuristic and matheuristic (hybrid exact and heuristic) procedures are proposed. A lagrangean heuristic addresses the capacitated lot-sizing problem with setup carryover and perishable products. A novel dynamic programming procedure is used to achieve the optimal solution of the uncapacitated single-item lot-sizing problem with setup carryover and perishable item. A heuristic, a fix-and-optimize procedure and an adaptive large neighbourhood search approach are proposed for the operational integrated production and distribution planning. Computational results on generated set of instances based on the literature show that the proposed methods yields competitive performances against other literature approaches. / Problemas de planejamento da produção são de suma importância no planejamento da cadeia de suprimentos, dando suporte às decisões da transformação de matérias-primas em produtos acabados. O dimensionamento de lotes em planejamento de produção é definido pelas decisões tático-operacionais relacionadas com o tamanho das ordens de produção e quando fabricá-las para satisfazer a demanda. Os objetivos destes problemas são geralmente de cunho econômico, tais como a redução de custos ou o aumento de lucros, embora outros aspectos possam ser considerados, tais como a qualidade do serviço ao cliente e a redução dos níveis de estoque. Problemas de dimensionamento de lotes são muito comuns em atividades de produção e um planejamento eficaz de tais atividades, estabelece uma clara vantagem à empresa em relação à concorrência. Para este objetivo, é necessária a consideração de características realistas do ambiente industrial e do produto. Para a modelagem matemática do problema, estas considerações são cruciais, embora sua inclusão resulte em formulações mais complexas. Embora os problemas de dimensionamento de lotes sejam bem conhecidos e amplamente estudados, várias características reais importantes não foram estudadas. Esta tese aborda, no contexto de dimensionamento de lotes, duas características muito relevantes: (a) preservação da preparação total e parcial; e (b) produtos perecíveis. A primeira permite que o estado de preparação de uma linha de produção seja mantido entre dois períodos consecutivos, mesmo que a linha de produção ainda não esteja totalmente pronta para o processamento de ordens de produção. A ultima característica determina que alguns produtos tem prazo de validade fixo, menor ou igual do que o horizonte de planejamento, o que afeta o planejamento da produção. Além disso, de acordo com a duração de sua vida útil, foram considerados dois tipos de produtos perecíveis: produtos com tempo de vida de médio e curto prazo. O ultimo caso resulta em um problema mais apertado do que o anterior, o que implica em planos de produção mais restritos. Isto pode exigir uma integração com outros processos da cadeia de suprimentos, tais como o planejamento de distribuição dos produtos acabados. Pesquisas sobre formulações matemáticas mais fortes e abordagens de solução para problemas de dimensionamento de lotes fornecem ferramentas valiosas para os planejadores de produção. O foco da tese reside no desenvolvimento de formulações de programação linear inteiro-mistas (MILP) para os problemas de dimensionamento de lotes, considerando as características mencionadas anteriormente. Novas técnicas de modelagem foram introduzidas, como a proposta de variáveis de preparação desagregadas e a consideração de decisões de dimensionamento de lotes ao invés de decisões de agrupamento de ordens de produção no problema integrado de planejamento de produção e distribuição. Estas formulações foram submetidas a experimentos computacionais em MILP-solvers de ponta. No entanto, a complexidade inerente destes problemas pode exigir abordagens de solução orientadas ao problema. Nesta tese, abordagens heurísticas, metaheurísticas e matheurísticas (híbrido de métodos exatos e heurísticos) foram propostas para os problemas discutidos. Uma heurística lagrangeana aborda o problema de dimensionamento de lotes com restrições de capacidade, preservação da preparação total e produtos perecíveis. Um novo procedimento de programação dinâmica e utilizado para encontrar a solução ótima do problema de dimensionamento de lotes de um único produto perecível, sem restrições de capacidade e preservação da preparação total. Uma heurística, um procedimento x-and-optimize e uma abordagem por buscas adaptativas em grande vizinhanças são propostas para o problema integrado de planejamento de produção e distribuição. Resultados computacionais em conjuntos de instâncias geradas com base na literatura mostram que os métodos propostos obtiveram performances competitivas com relação a outras abordagens da literatura.

Networked Control Systems (NCS) are distributed control systems where the sensor signals to the controllers and the control data to the actuators are enclosed in messages and sent over a communication network. On the one hand, the design of an NCS requires ensuring the stability of the control system and achieving system response that is as close as possible to that of an ideal system which demands network resources. On the other hand, these resources are limited and have to be allocated efficiently to accommodate for future system extensions as well as applications other than control purpose. Furthermore the NCS design parameters for the control system messages and the message transmission over the network are interdependent. In this thesis, we propose &ldquo / Integrated NCS Design (INtERCEDE: Integrated NEtwoRked Control systEm DEsign)&rdquo / a novel algorithmic approach for the design of NCS which ensures the stability of the control system, brings system response to that of an ideal system v as close as desired and conserves network bandwidth at the same time. The core of INtERCEDE is a bargaining game approach which iteratively calculates the message parameters and network service parameters. Our experimental results demonstrate the operation of INtERCEDE and how it computes the optimal design parameters for the example NCS.

Thesis (Ph. D.)--Ohio State University, 2007. / Full text release at OhioLINK's ETD Center delayed at author's request

M.Ing. / The Internet is evolving into a global communication infrastructure that is expected to support an overabundance of new applications such as IP telephony, interactive TV, and e-commerce. The existing best effort service is no longer sufficient. It is not enough to provide differentiated services and to meet QoS requirements of these different traffic types. As a result, there is an urgent need to provide more services that are powerful such as guaranteed services, flow protection etc, merged in one IP network, referred to as Integrated Services Packet-Switching Network (ISPN) in this thesis. To provide these services, QoS aware network architectures are required to implement the services. This dissertation presents a survey on two network architectures: Fair Queuing (FQ) and Scalable Core (SCORE), which attempt to provide QoS solutions in ISPN. We theoretically analyse scheduling as an important element in providing QoS in these architectures. The important thread in scheduling is performance and implementation complexity. SCORE based scheduling have less implementation complexity but cannot exactly match the high performance of FQ solutions, which suffer implementation complexity. The contribution of this work is a feedback protocol that minimises congestion in SCORE scheduling scheme called Core stateless fair queuing (CSFQ). The flow rates are adjusted by sending rate signal to a transmitting node from a receiving node, to adjust ill-behaved flow rate during congestion to a fair share rate of receiving node. We use CSFQ based theoretical analysis and simulations to demonstrate the performance of the feedback protocol.

Typically, a real-time system consists of a controlling system (i.e., a computer) and a controlled system (i.e., the environment). Real-time systems are those systems where correctness depends on two aspects: i) the logical result of computation and, ii) the time in which results are produced. It is essential to guarantee meeting timing constraints for this kind of systems to operate correctly. Missing deadlines in many cases -- in so-called hard real-time systems -- is associated with economic loss or loss of human lives and must be avoided under all circumstances. On the other hand, there is a trend towards consolidating software functions onto fewer processors in different domains such as automotive systems and avionics with the aim of reducing costs and complexity. Hence, applications with different levels of criticality that used to run in isolation now start sharing processors. As a result, there is a need for techniques that allow designing such mixed-criticality (MC) systems -- i.e., real-time systems combining different levels of criticality -- and, at the same time, complying with certification requirements in the different domains. In this research, we study the problem of scheduling MC tasks under EDF (Earliest Deadline First) and propose new approaches to improve scheduling techniques. In particular, we consider that a mix of low-criticality (LO) and high-criticality (HI) tasks are scheduled on one processor. While LO tasks can be modeled by minimum inter-arrival time, deadline, and worst-case execution time (WCET), HI tasks are characterized by two WCET parameters: an optimistic and a conservative one. Basically, the system operates in two modes: LO and HI mode. In LO mode, HI tasks run for no longer than their optimistic execution budgets and are scheduled together with the LO tasks. The system switches to HI mode when one or more HI tasks run for more than their conservative execution budgets. In this case, LO tasks are immediately discarded so as to be able of accommodating the increase in HI execution demand. We propose an exact test for mixed-criticality EDF, which increases efficiency and reliability when compared with the existing approaches from the literature. On this basis, we further derive approximated tests with less complexity and, hence, a reduced running time that makes them more suitable for online checks.:Contents 1. Introduction 1 1.1. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3. Structure of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2. Concepts, Models and Assumptions 7 2.1. Real-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1. Tasks Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2. Scheduling Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1. Feasibility versus Schedulability . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2. Schedulability Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3. Mixed-Criticality Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4. Basic Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5. The Earliest Deadline First Algorithm . . . . . . . . . . . . . . . . . . . . . . 13 2.5.1. EDF-VD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.5.2. Mixed-Criticality EDF . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.5.3. Demand Bound Function . . . . . . . . . . . . . . . . . . . . . . . . . 16 3. Related Work 17 3.1. Uniprocessor Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.1. Uniprocessor Scheduling Based on EDF . . . . . . . . . . . . . . . . . 18 3.2. Multiprocessor Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.1. Multiprocessor Scheduling Based on EDF . . . . . . . . . . . . . . . . 20 4. Introducing Utilization Caps 23 4.1. Introducing Utilization Caps . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1.1. Fixed utilization caps . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.1.2. Optimized utilization caps . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2. Findings of this Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5. Bounding Execution Demand under Mixed-Criticality EDF 29 5.1. Bounding Execution Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2. Analytical Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2.1. The GREEDY Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2.2. The ECDF Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3. Finding Valid xi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 5.4. Findings of this Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6. Approximating Execution Demand Bounds 41 6.1. Applying Approximation Techniques . . . . . . . . . . . . . . . . . . . . . . . 41 6.2. Devi’s Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.2.1. Per-task deadline scaling . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6.2.2. Uniform deadline scaling . . . . . . . . . . . . . . . . . . . . . . . . . . 44 6.2.3. Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 6.3. Findings of this Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7. Evaluation and Results 49 7.1. Mixed-Criticality EDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.2. Obtaining Test Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.2.1. The Case Di = Ti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 7.2.2. The Case Di ≤ Ti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 7.3. Weighted schedulability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 7.4. Algorithms in this Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . 51 7.4.1. The EDF-VD and DEDF-VD Algorithms . . . . . . . . . . . . . . . . 51 7.4.2. The GREEDY algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 52 7.4.3. The ECDF algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 7.5. Evaluation of Utilization Caps . . . . . . . . . . . . . . . . . . . . . . . . . . 53 7.5.1. 10 tasks per task set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 7.5.2. 20 tasks per task set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 7.5.3. 50 tasks per task set . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 7.5.4. Comparison of runtime . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7.6. Evaluation of Execution Demand Bounds . . . . . . . . . . . . . . . . . . . . 61 7.6.1. Comparison for sets of 10 tasks . . . . . . . . . . . . . . . . . . . . . . 61 7.6.2. Comparison for sets of 20 tasks . . . . . . . . . . . . . . . . . . . . . . 64 7.7. Evaluation of Approximation Techniques . . . . . . . . . . . . . . . . . . . . . 67 7.7.1. Schedulability curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 7.7.2. Weighted schedulability . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.7.3. Comparison of runtime . . . . . . . . . . . . . . . . . . . . . . . . . . 72 7.8. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 8. Conclusion and Future Work 77 8.1. Outlook/Future Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Bibliography 83 A. Introduction 91 A.1. Multiple Levels of Criticality . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 A.1.1. Ordered mode switches . . . . . . . . . . . . . . . . . . . . . . . . . . 91 A.1.2. Unordered mode switches . . . . . . . . . . . . . . . . . . . . . . . . . 93 B. Evaluation and Results 95 B.1. Uniform Distribution for Task Periods . . . . . . . . . . . . . . . . . . . . . . 95

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