By Vladimir V. Mityushev, Michael Ruzhansky
The e-book contains lectures given via the plenary and key audio system on the ninth foreign ISAAC Congress held 2013 in Krakow, Poland. The contributions deal with contemporary advancements in research and surrounding parts, bearing on subject matters from the idea of partial differential equations, functionality areas, scattering, chance idea, and others, in addition to purposes to biomathematics, queueing versions, fractured porous media and geomechanics.
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We discuss here the means used to analyse transient states in queueing models. In computer applications a mathematical model is useful only when it furnishes quantitative results. Therefore practical issues related to numerical side of models are of importance and are here discussed. We present three approaches—Markov models solved numerically, fluid flow approximation and diffusion approximation. A particular importance is given to the latter as the author has here over 20 year experience in development and application of this method.
Lond. A 469, 20120533 (2013) Queueing Models for Performance Evaluation of Computer Networks—Transient State Analysis Tadeusz Czachórski Abstract Queueing theory is a useful tool in design of computer networks and their performance evaluation. The literature concerning this subject is abundant. However, it is in general limited to the analysis of steady states. It means that flows of customers considered in models are constant and obtained solutions do not depend on time. It is in glaring contrast with the flows observed in real networks where the perpetual changes of traffic intensities are due to the nature of users, sending variable quantities of data, cf.
Indiana Univ. Math. J. 52(4), 981–990 (2003) 12. T. Varopoulos, Aspects of probabilistic Littlewood-Paley theory. J. Funct. Anal. 38, 25–60 (1980) 13. F. T. Varopoulos, Les transformations de Riesz et les intégrales stochastiques. C. R. Acad. Sci. Paris Sér. I. Math. 289, A13–A16 (1979) 14. B. Davies, Heat Kernels and Spectral Theory (Cambridge University Press, Cambridge, 1989) 15. A. Grigor’yan, A. Telcs, Two-sided estimates of heat kernels on metric measure spaces. Ann. Probab. 40, 1212–1284 (2012) 40 D.
Analytic Methods in Interdisciplinary Applications by Vladimir V. Mityushev, Michael Ruzhansky
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