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We present an analysis framework for performance evaluation of large-scale resource-bound (LSRB) computer systems. LSRB systems are those whose resources are continually in demand to serve resource users, who appear in large populations and cause high contention. In these systems, the delivery of quality service is crucial, even in the event of resource failure. Therefore, various techniques have been developed for evaluating their performance. In this thesis, we focus on the technique of quantitative modelling, where in order to study a system, first its model is constructed and then the system’s behaviour is analysed via the model. A number of high level formalisms have been developed to aid the task of model construction. We focus on PEPA, a stochastic process algebra that supports compositionality and enables us to easily build complex LSRB models. In spite of this advantage, however, the task of analysing LSRB models still poses unresolved challenges. LSRB models give rise to very large state spaces. This issue, known as the state space explosion problem, renders the techniques based on discrete state representation, such as numerical Markovian analysis, computationally expensive. Moreover, simulation techniques, such as Gillespie’s stochastic simulation algorithm, are also computationally demanding, as numerous trajectories need to be collected. Furthermore, as we show in our first contribution, the techniques based on the mean-field theory or fluid flow approximation are not readily applicable to this case. In LSRB models, resources are not assumed to be present in large populations and models exhibit highly noisy and stochastic behaviour. Thus, the mean-field deterministic behaviour might not be faithful in capturing the system’s randomness and is potentially too crude to show important aspects of their behaviours. In this case, the modeller is unable to obtain important performance indicators, such as the reliability measures of the system. Considering these limitations, we contribute the following analytical methods particularly tailored to LSRB models. First, we present an aggregation method. The aggregated model captures the evolution of only the system’s resources and allows us to efficiently derive a probability distribution over the configurations they experience. This distribution provides full faithfulness for studying the stochastic behaviour of resources. The aggregation can be applied to all LSRB models that satisfy a syntactic aggregation condition, which can be quickly checked syntactically. We present an algorithm to generate the aggregated model from the original model when this condition is satisfied. Second, we present a procedure to efficiently detect time-scale near-complete decomposability (TSND). The method of TSND allows us to analyse LSRB models at a reduced cost, by dividing their state spaces into loosely coupled blocks. However, one important input is a partition of the transitions defined in the model, categorising them into slow or fast. Forming the necessary partition by the analysis of the model’s complete state space is costly. Our process derives this partition efficiently, by relying on a theorem stating that our aggregation preserves the original model’s partition and therefore, it can be derived by an efficient reachability analysis on the aggregated state space. We also propose a clustering algorithm to implement this reachability analysis. Third, we present the method of conditional moments (MCM) to be used on LSRB models. Using our aggregation, a probability distribution is formed over the configurations of a model’s resources. The MCM outputs the time evolution of the conditional moments of the marginal distribution over resource users given the configurations of resources. Essentially, for each such configuration, we derive measures such as conditional expectation, conditional variance, etc. related to the dynamics of users. This method has a high degree of faithfulness and allows us to capture the impact of the randomness of the behaviour of resources on the users. Finally, we present the advantage of the methods we proposed in the context of a case study, which concerns the performance evaluation of a two-tier wireless network constructed based on the femto-cell macro-cell architecture.

Considerando-se o contexto de gerenciamento energético em grades móveis, neste trabalho foram propostos dois algoritmos de escalonamento (Maximum Regret e Greedy) que, além de minimizar o consumo de energia, visam assegurar o cumprimento dos requisitos de qualidade de serviço das aplicações submetidas pelos usuários. Tais algoritmos foram projetados a partir de soluções heurísticas para o problema de escalonamento ciente de consumo de energia em grades móveis, que foi modelado como um problema de otimização envolvendo variáveis binárias. Por meio de experimentos, que consideraram tanto cenários estáticos quanto dinâmicos, foi demonstrada a viabilidade dos algoritmos de escalonamento propostos em relação à redução do consumo de energia. Em seu pior caso, o algoritmo Maximum Regret foi 12,18% pior que o referencial determinado pela melhor solução do solver Gurobi; já no pior caso do algoritmo Greedy, tal diferença foi de apenas 8,14% / Considering the context of energy management in mobile grids, this work proposes two scheduling algorithms (Maximum Regret and Greedy) that aim not only to reduce the energy consumption of the mobile devices, but also to ensure the QoS (Quality of Service) requirements of the running applications. These algorithms were designed based on heuristics for the energy aware scheduling problem in mobile grids, which was modeled as an optimization problem with integer variables. The performances of the proposed scheduling algorithms were evaluated by an extensive set of experiments, which demonstrated the feasibility of the adopted approach regarding energy consumption minimization. In its worst case, the Maximum Regret algorithm was 12.18% worse than the best solution provided by the Gurobi solver. While in the Greedys worst case the performance difference was just 8.14%

Considerando-se o contexto de gerenciamento energético em grades móveis, neste trabalho foram propostos dois algoritmos de escalonamento (Maximum Regret e Greedy) que, além de minimizar o consumo de energia, visam assegurar o cumprimento dos requisitos de qualidade de serviço das aplicações submetidas pelos usuários. Tais algoritmos foram projetados a partir de soluções heurísticas para o problema de escalonamento ciente de consumo de energia em grades móveis, que foi modelado como um problema de otimização envolvendo variáveis binárias. Por meio de experimentos, que consideraram tanto cenários estáticos quanto dinâmicos, foi demonstrada a viabilidade dos algoritmos de escalonamento propostos em relação à redução do consumo de energia. Em seu pior caso, o algoritmo Maximum Regret foi 12,18% pior que o referencial determinado pela melhor solução do solver Gurobi; já no pior caso do algoritmo Greedy, tal diferença foi de apenas 8,14% / Considering the context of energy management in mobile grids, this work proposes two scheduling algorithms (Maximum Regret and Greedy) that aim not only to reduce the energy consumption of the mobile devices, but also to ensure the QoS (Quality of Service) requirements of the running applications. These algorithms were designed based on heuristics for the energy aware scheduling problem in mobile grids, which was modeled as an optimization problem with integer variables. The performances of the proposed scheduling algorithms were evaluated by an extensive set of experiments, which demonstrated the feasibility of the adopted approach regarding energy consumption minimization. In its worst case, the Maximum Regret algorithm was 12.18% worse than the best solution provided by the Gurobi solver. While in the Greedys worst case the performance difference was just 8.14%