The Use of Imitation Models at Developing and Introducing Information-Control Systems

Imitation models for computing the environmental water pollution level depending on the intensity of pollution sources created by the author over the years are presented. For this purpose, an additive model of a non-stationary random process is considered. For the modeling of its components, models that consider only dilution and self-purification processes are proposed for waste water and three-dimensional turbulent diffusion equations for river waters, and multidimensional Gaussian Markov series are proposed for modeling the random component. The purpose, the capabilities and the peculiarities of such imitation models are discussed taking into account the peculiarities of the water objects. The modular principle of creating imitation models is proposed to facilitate their development and use.

On One Analytical Model of a Probability Estimation of Quality and Efficiency of Functioning of Complex Technical Queuing Systems

The work is dedicated to the development of analytical model of probability estimation of reliability, productivity, quality and efficiency of functioning of the complex technical queuing system consisting of the arbitrary number of marked groups of the service devises (channels, facilities, servers) differing with reliable characteristics (parameters of refusals and restorations) of forming their composition (also of arbitrary number) marked, identical, unreliable and restorable serving channels in which for serving come in requirements with intensities depending on marking of channels. In the considered system it is supposed that the currents of refusals of serving devices and currents of coming requirements are subdued to Poisson, and the currents of restorations of refused devices and the currents of services of coming requirements—exponential laws of distribution of probabilities. A stochastic process of transfers of a system by that is Markovian process with continuous time and discrete states. Correlations linking the basic parameters and exit characteristics of the systems of the pointed out type are obtained in a view of probabilities of the system location in the given moment of time in one of the possible states.

On Ordinary and Standard Products of Infinite Family of σ-finite Measures and Some of Their Applications

我们介绍有限措施的平常、标准的产品的观点并且证明他们的存在。这条途径允许我们构造 Haar 措施的平常、标准的产品的不变的延期。特别地，我们上构造平常、标准的 Lebesgue 措施的翻译不变的延期吗？并且 Rogers-Fremlin 上测量？，分别地以便与这些措施联系的伪度量标准空格的拓扑的重量是最大的(即， 2 c ) 。我们也解决在 Banach 空格担心一致措施的存在的一些 Fremlin 问题。