Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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.


References [Enhancements On Off] (What's this?)

  • [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

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