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In the paper a Semi-markov process is used to construct a general model of complex industrial systems’ operation processes. Main parameters of this model are defined and its main characteristics are determined as well. In particular case, for a gantry crane, the operation states are defined, the relationships between them are fixed and particular model of its operation process is constructed and finally its main characteristics are determined.
We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called “times.”
The paper objectives are to present the methods and tools useful in the statistical identifying unknown parameters of the operation models of complex technical systems and to apply them in the maritime industry. There are presented statistical methods of determining unknown parameters of the semi-markov model of the complex technical system operation processes. There is also presented the chi-square goodness-of-fit test applied to verifying the distributions of the system operation process conditional sojourn times in the particular operation states. Applications of these tools to identifying and predicting the operation characteristics of a ferry operating at the Baltic Sea waters are presented as well.
This paper investigates an N-policy GI/M/1 queue in a multi-phase service environment with disasters, where the system tends to suffer from disastrous failures while it is in operative service environments, making all present customers leave the system simultaneously and the server stop working completely. As soon as the number of customers in the queue reaches a threshold value, the server resumes its service and moves to the appropriate operative service environment immediately with some probability. We derive the stationary queue length distribution, which is then used for the computation of the Laplace– Stieltjes transform of the sojourn time of an arbitrary customer and the server’s working time in a cycle. In addition, some numerical examples are provided to illustrate the impact of several model parameters on the performance measures.
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