Parametric synthesis of statistical communication nets
Authors:
H. Frank and S. L. Hakimi
Journal:
Quart. Appl. Math. 27 (1969), 105-120
MSC:
Primary 94.30
DOI:
https://doi.org/10.1090/qam/256777
MathSciNet review:
256777
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Abstract: The traffic within the branches of a communication network is often a random variable with an approximate multivariate normal distribution. The analysis of such systems has been discussed in a previous paper. In this paper, we consider the optimum synthesis problem. Nonlinear and linear programming is used to guarantee that a given flow rate probability between a specified pair of terminals is achieved. In particular, a Uniformly Most Powerful Statistical Test provides the basis for an optimum synthesis procedure that appears to be very efficient. The procedure is formulated as a concave program with quadratic and linear constraints.
H. Frank and S. L. Hakimi, Probabilistic flows through a communication network, IEEE Trans. on Circuit Theory, Vol. CT-12, No. 3, pp. 413–414, Sept. 1965
H. Frank and S. L. Hakimi, On the optimum synthesis of statistical communication nets—pseudoparametric techniques, J. Franklin Inst. 284, 407–467 (1967)
- H. Frank and S. L. Hakimi, Parametric analysis of statistical communication nets, Quart. Appl. Math. 26 (1968), 249–263. MR 233616, DOI https://doi.org/10.1090/S0033-569X-1968-0233616-2
I. T. Frisch, Optimization of communication nets with switching, J. Franklin Intitute, 275, 405-430 (1963)
- G. Hadley, Nonlinear and dynamic programming, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964. MR 0173543
M. Abramowitz and L. A. Stegun (Editors), Handbook of mathematical functions, National Bureau of Standards, Applied Math. Series 55, 1964, p. 933
N. Deo and S. L. Hakimi, Minimum cost increase of the terminal capacities of a communication net, IEEE Trans. on Comm. Tech., Vol. COM-14, No. 1, pp. 63-64, Feb. (1966)
- Charles E. Clark, The greatest of a finite set of random variables, Operations Res. 9 (1961), 145–162. MR 125604, DOI https://doi.org/10.1287/opre.9.2.145
- William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York; Chapman and Hall, Ltd., London, 1957. 2nd ed. MR 0088081
- F. R. Gantmacher, Matrizenrechnung. II. Spezielle Fragen und Anwendungen, Hochschulbücher für Mathematik, Bd. 37, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959 (German). MR 0107647
H. Frank and S. L. Hakimi, Probabilistic flows through a communication network, IEEE Trans. on Circuit Theory, Vol. CT-12, No. 3, pp. 413–414, Sept. 1965
H. Frank and S. L. Hakimi, On the optimum synthesis of statistical communication nets—pseudoparametric techniques, J. Franklin Inst. 284, 407–467 (1967)
H. Frank and S. L. Hakimi, Parametric analysis of statistical communication nets, Quart. Appl. Math. XXVI, 249–263 (1968)
I. T. Frisch, Optimization of communication nets with switching, J. Franklin Intitute, 275, 405-430 (1963)
G. Hadley, Nonlinear and dynamic programming, Addison-Wesley, Reading, Mass., 1964
M. Abramowitz and L. A. Stegun (Editors), Handbook of mathematical functions, National Bureau of Standards, Applied Math. Series 55, 1964, p. 933
N. Deo and S. L. Hakimi, Minimum cost increase of the terminal capacities of a communication net, IEEE Trans. on Comm. Tech., Vol. COM-14, No. 1, pp. 63-64, Feb. (1966)
C. E. Clark, The greatest of a finite set of random variables, Operations Research, 9, 145-162 (1961)
W. Feller, An introduction to probability theory and its applications, Vol. 1, Wiley, New York, 1957, pp. 177-178
F. R. Gantmacher, Matrix theory, Vol. 1, Chelsea, New York, 1959, pp. 299-304
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© Copyright 1969
American Mathematical Society
