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In recent years, the problem of capacity allocation for a label switched patch (LSP) in a multiprotocol label switched (MPLS) network has received great attention due to its relevance in the context of traffic control. In this paper, the problem of capacity allocation is formulated as an optimal control problem and its solution is obtained by assum...
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This paper strives for domain generalization, where models are trained exclusively on source domains before being deployed at unseen target domains. We follow the strict separation of source training and target testing but exploit the value of the unlabeled target data itself during inference. We make three contributions. First, we propose probabil...
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The concepts of Effective Information Horizon (EIH) and Effective Information Space (EIS) reflect the extent to which information is required for optimally controlling offline dynamic systems in stochastic environments. These concepts can be applied to overcome the difficulties involved in forecasting that arise when considering future information. Two approaches are utilized for modeling a given dynamic system. The first, denoted as pseudo-stochastic, is basically deterministic and considers the flow of uncertain future events by a superposition of the distribution functions of an event’s occurrence time. The second approach, the general stochastic model, considers all possible future scenarios. Several applications that are presented illustrate that when using only partial information for determining optimal control, the performance of the dynamic system is almost identical to that when using full information. The applications also illustrate that ignoring information beyond the planning horizon leads to significant performance loss and may violate the constraints of a control problem.
Abstract In this study, which is both analytical and numerical, we compute the effective information horizon (EIH), i.e., the minimal time interval over which future information is relevant for optimal control and for measuring the performance of a single part-type production system. Optimal control modeling and process solving, which consider aspects of decision making with limited forecast, are exemplified by a single part-type production system. Specifically, the analysis reveals practical situations in which there is both a performance loss as well as feasibility violation when only information expected within the planning horizon is considered. The analysis is carried out by developing a pseudo-stochastic model. We follow previous “pseudo-stochastic” approaches that solve stochastic control problems by using deterministic, optimal control methods. However, we model the expected influences of all future events, including those that are beyond the planning horizon, as encapsulated by their density functions and not only by their mean values.
In this paper properties of monotone increasing behavior along the diagonals are exhibited for special classes of Toeplitz and modified Toeplitz matrices. By exploiting these properties, approximations are proposed for the inverses of these matrices, which have a large number of zero diagonals. An in-depth analysis is performed about the approximation level obtainable correspondingly to the number of diagonals set to zero. An application of the results in the context of optimal control is presented to show the advantage achievable by the proposed approximation with respect to the amount of information required.
