Generalized Priority Systems. Analytical Results and Numerical Algorithms

A class of priority systems with non-zero switching times, referred as generalized priority systems, is considered. Analytical results regarding the distribution of busy periods, queue lengths and various auxiliary characteristics are presented. These results can be viewed as generalizations of the Kendall functional equation and the Pollaczek-Khintchin transform equation, respectively. Numerical algorithms for systems’ busy periods and traffic coefficients are developed. ACM Computing Classification System (1998): 60K25.

The Information-analytical System for Diagnostics of Aircraft Navigation Units

The operation of technical processes requires increasingly advanced supervision and fault diagnostics to improve reliability and safety. This paper gives an introduction to the field of fault detection and diagnostics and has short methods classification. Growth of complexity and functional importance of inertial navigation systems leads to high losses at the equipment refusals. The paper is devoted to the INS diagnostics system development, allowing identifying the cause of malfunction. The practical realization of this system concerns a software package, performing a set of multidimensional information analysis. The project consists of three parts: subsystem for analyzing, subsystem for data collection and universal interface for open architecture realization. For a diagnostics improving in small analyzing samples new approaches based on pattern recognition algorithms voting and taking into account correlations between target and input parameters will be applied. The system now is at the development stage.

Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.