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.

**[1]**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**[2]**H. Frank and S. L. Hakimi,*On the optimum synthesis of statistical communication nets--pseudoparametric techniques*, J. Franklin Inst.**284**, 407-467 (1967)**[3]**H. Frank and S. L. Hakimi,*Parametric analysis of statistical communication nets*, Quart. Appl. Math.**26**(1968), 249–263. MR**0233616**, https://doi.org/10.1090/S0033-569X-1968-0233616-2**[4]**I. T. Frisch,*Optimization of communication nets with switching*, J. Franklin Intitute,**275**, 405-430 (1963)**[5]**G. Hadley,*Nonlinear and dynamic programming*, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964. MR**0173543****[6]**M. Abramowitz and L. A. Stegun (Editors),*Handbook of mathematical functions*, National Bureau of Standards, Applied Math. Series 55, 1964, p. 933**[7]**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)**[8]**Charles E. Clark,*The greatest of a finite set of random variables*, Operations Res.**9**(1961), 145–162. MR**0125604****[9]**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****[10]**F. R. Gantmacher,*The theory of matrices. Vols. 1, 2*, Translated by K. A. Hirsch, Chelsea Publishing Co., New York, 1959. MR**0107649**

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DOI:
https://doi.org/10.1090/qam/256777

Article copyright:
© Copyright 1969
American Mathematical Society