Parametric analysis of statistical communication nets
Authors:
H. Frank and S. L. Hakimi
Journal:
Quart. Appl. Math. 26 (1968), 249-263
MSC:
Primary 94.10
DOI:
https://doi.org/10.1090/qam/233616
MathSciNet review:
233616
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Abstract: The existing traffic within the branches of a communication net can often be assumed to be normally distributed random variables. A natural problem is to determine the probability that a particular flow rate between a pair of stations can be attained. If this probability is too small, it is necessary to improve the net with minimum cost. In this paper, analysis techniques on which effective synthesis procedures can be based are developed. An exact method for evaluating the flow rate probability is obtained as well as upper and lower bounds. Monte Carlo techniques are applied and the flow rate is seen to be approximately normally distributed. A method of finding the approximate mean and variance of the flow rate is given, as well as a Uniformly Most Powerful Invariant Statistical test.
H. Frank and S. L. Hakimi, Probabilistic flows through a communication network, IEEE Trans, on Circuit Theory, CT-12, No. 3, 413–414 (1965)
H. Frank and S. L. Hakimi, On the optimum synthesis of statistical communications nets, J. Franklin Institute 284,407-416 (1967)
- H. Frank and S. L. Hakimi, Parametric synthesis of statistical communication nets, Quart. Appl. Math. 27 (1969), 105–120. MR 256777, DOI https://doi.org/10.1090/S0033-569X-1969-0256777-1
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F. R. Gantmacher, The theory of matrices, Vol. I, Chelsea, New York, 1960
- Shanti S. Gupta, Probability integrals of multivariate normal and multivariate $t$, Ann. Math. Statist. 34 (1963), 792–828. MR 152068, DOI https://doi.org/10.1214/aoms/1177704004
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H. Frank and S. L. Hakimi, Probabilistic flows through a communication network, IEEE Trans, on Circuit Theory, CT-12, No. 3, 413–414 (1965)
H. Frank and S. L. Hakimi, On the optimum synthesis of statistical communications nets, J. Franklin Institute 284,407-416 (1967)
H. Frank and S. L. Hakimi, Parametric synthesis of statistical communication nets, Quart. Appl. Math. (to appear)
W. Feller, An introduction to probability theory and its applications, Vol. 1, Wiley, New York, 1957, p. 177
M. Fisz, Probability theory and mathematical statistics, Wiley, New York, 1963
H. Cramér, Mathematical methods of statistics, Princeton Univ. Press, Princeton, N. J., 1946
L. R. Ford, Jr., and D. R. Fulkerson, Flows in networks, Princeton Univ. Press, Princeton, N. J., 1962
F. R. Gantmacher, The theory of matrices, Vol. I, Chelsea, New York, 1960
S. Gupta, Probability integrals of multivariate normal and multivariate t, Ann. Math. Stat. 34, 792–828 (1963)
C. E. Clark, The greatest of a finite set of random variables, Operations Research, 145–162 (1961)
E. L. Lehmann, Testing statistical hypotheses, Wiley, New York, 1959
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Article copyright:
© Copyright 1968
American Mathematical Society