Three new decomposition methods are developed for the exact analysis of stochastic multi-facility blocking models of the product-form type. The first is a basic decomposition algorithm that reduces the analysis of blocking probabilities to that of two separate subsystems. The second is a generalized M-subsystem decomposition method. The third is a more elaborate and efficient incremental decomposition technique. All of the algorithms exploit the sparsity of locality that can be found in the demand matrix of a system. By reducing the analysis to that of a set of subsystems, the overall dimensionality of the problem is diminished and the computational requirements are reduced significantly. This enables the efficient computation of blocking probabilities in large systems. Several numerical examples are provided to illustrate the computational savings that can be realized.

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Smartwatch battery limitations are one of the biggest hurdles to their acceptability in the consumer market. To our knowledge, despite promising studies analyzing smartwatch battery data, there has been little research that has analyzed the battery usage of a diverse set of smartwatches in a real-world setting. To address this challenge, this paper utilizes a smartwatch dataset collected from 832 real-world users, including different smartwatch brands and geographic locations. First, we employ clustering to identify common patterns of smartwatch battery utilization; second, we introduce a transparent low-parameter convolutional neural network model, which allows us to identify the latent patterns of smartwatch battery utilization. Our model converts the battery consumption rate into a binary classification problem; i.e., low and high consumption. Our model has 85.3% accuracy in predicting high battery discharge events, outperforming other machine learning algorithms that have been used in state-of-the-art research. Besides this, it can be used to extract information from filters of our deep learning model, based on learned filters of the feature extractor, which is impossible for other models. Third, we introduce an indexing method that includes a longitudinal study to quantify smartwatch battery quality changes over time. Our novel findings can assist device manufacturers, vendors and application developers, as well as end-users, to improve smartwatch battery utilization.