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.

Advanced monitoring of the spatio-temporal distribution of process parameters in large-scale vessels and containers such as stirred chemical or bioreactors offers a high potential for the investigation and further optimization of plants and embedded processes. This applies especially to large-scale fermentation biogas reactors where the process performance including the biological processes highly depend on mixing parameters of the complex bio-substrates. Sufficient mixing is a basic requirement for a stable operation of the process and adequate process performance. However, this condition is rarely met in agricultural biogas plants and the process efficiency is often reduced dramatically by inhomogeneities in the agitated vessels. Without a doupt, investigation and monitoring of biochemical parameters, such as the fermentation rate, pH distribution as well as O2 and CO2 concentration is of great importance. Nevertheless, also understanding of non-biological parameters, such as fluid dynamics (flow velocity profiles, circulation times), suspension mixing (homogeneity, location of dead zones and short-circuits) and heat transfer (temperature profiles), is necessary to analyze the impact of mixing on the biological system and also to improve the process efficiency. However, in most industrial scale applications the acquisition of these parameters and their spatial distributions in the large-scale vessels is hampered by the limited access to the process itself, because sensor mounting or cable connections are not feasible or desired. Therefore, state of the art instrumentation of such reactors is commonly limited to few spatial positions where it is doubtfully assumed that the measured parameters are representative for the whole reaction mixture. In this work, a concept of flow following sensor particles was developed. The sensor particles allow long-term measurement of spatially distributed process parameters in the chemically and mechanically harsh environments of agitated industrial vessels. Each sensor particle comprises of an onboard measurement electronics that logs the signals of measurement devices, namely temperature, absolute pressure (immersion depth, axial position) and 3D acceleration. The whole electronics is enclosed in a robust neutrally buoyant capsule (equivalent diameter 58.2 mm; sphericity 0.91), to allow free movement with the flow. The sensor particles were tested in pilot fermenters under comparable flow conditions of biogas fermenters. The experiments proved the applicability of the sensor particles and the robustness to resist the harsh environments of mixing processes. Moreover, the results show the capabilities of the sensor particles to monitor the internal conditions of the vessel correctly and thus deliver significant information about the flow regime. Therefore effects of liquid rheology, vessel geometry, impeller speed and axial impeller position on the macro-mixing process were properly detected. Evaluation of the impeller efficiency and the mixing processes was done based on mixing homogeneity, location of dead zones, axial velocity profiles, circulation time distributions as well as average circulation times, acceleration spectra and temperature profiles that were extracted from the measured data. Furthermore, it is shown, that parameters of mixing models such as circulation number, impeller head, PECLÉT-number and variance of suspended solid particles can be estimated from the measured data. The main achievement of this work is therefore the development and validation of instrumented flow followers for the investigation of macro-mixing effects in agitated vessels. The sensor particles show potential for employment to real applications such as biogas fermenters or large bioreactors and to monitor and improve the mixing and heating regimes.

Advanced monitoring of the spatio-temporal distribution of process parameters in large-scale vessels and containers such as stirred chemical or bioreactors offers a high potential for the investigation and further optimization of plants and embedded processes. This applies especially to large-scale fermentation biogas reactors where the process performance including the biological processes highly depend on mixing parameters of the complex bio-substrates. Sufficient mixing is a basic requirement for a stable operation of the process and adequate process performance. However, this condition is rarely met in agricultural biogas plants and the process efficiency is often reduced dramatically by inhomogeneities in the agitated vessels. Without a doupt, investigation and monitoring of biochemical parameters, such as the fermentation rate, pH distribution as well as O2 and CO2 concentration is of great importance. Nevertheless, also understanding of non-biological parameters, such as fluid dynamics (flow velocity profiles, circulation times), suspension mixing (homogeneity, location of dead zones and short-circuits) and heat transfer (temperature profiles), is necessary to analyze the impact of mixing on the biological system and also to improve the process efficiency. However, in most industrial scale applications the acquisition of these parameters and their spatial distributions in the large-scale vessels is hampered by the limited access to the process itself, because sensor mounting or cable connections are not feasible or desired. Therefore, state of the art instrumentation of such reactors is commonly limited to few spatial positions where it is doubtfully assumed that the measured parameters are representative for the whole reaction mixture. In this work, a concept of flow following sensor particles was developed. The sensor particles allow long-term measurement of spatially distributed process parameters in the chemically and mechanically harsh environments of agitated industrial vessels. Each sensor particle comprises of an onboard measurement electronics that logs the signals of measurement devices, namely temperature, absolute pressure (immersion depth, axial position) and 3D acceleration. The whole electronics is enclosed in a robust neutrally buoyant capsule (equivalent diameter 58.2 mm; sphericity 0.91), to allow free movement with the flow. The sensor particles were tested in pilot fermenters under comparable flow conditions of biogas fermenters. The experiments proved the applicability of the sensor particles and the robustness to resist the harsh environments of mixing processes. Moreover, the results show the capabilities of the sensor particles to monitor the internal conditions of the vessel correctly and thus deliver significant information about the flow regime. Therefore effects of liquid rheology, vessel geometry, impeller speed and axial impeller position on the macro-mixing process were properly detected. Evaluation of the impeller efficiency and the mixing processes was done based on mixing homogeneity, location of dead zones, axial velocity profiles, circulation time distributions as well as average circulation times, acceleration spectra and temperature profiles that were extracted from the measured data. Furthermore, it is shown, that parameters of mixing models such as circulation number, impeller head, PECLÉT-number and variance of suspended solid particles can be estimated from the measured data. The main achievement of this work is therefore the development and validation of instrumented flow followers for the investigation of macro-mixing effects in agitated vessels. The sensor particles show potential for employment to real applications such as biogas fermenters or large bioreactors and to monitor and improve the mixing and heating regimes.