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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**H. Frank and S. L. Hakimi,*Probabilistic flows through a communication network*, IEEE Trans, on Circuit Theory,**CT-12**, No. 3, 413-414 (1965)**[2]**H. Frank and S. L. Hakimi,*On the optimum synthesis of statistical communications nets*, J. Franklin Institute 284,407-416 (1967)**[3]**H. Frank and S. L. Hakimi,*Parametric synthesis of statistical communication nets*, Quart. Appl. Math.**27**(1969), 105–120. MR**0256777**, https://doi.org/10.1090/S0033-569X-1969-0256777-1**[4]**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****[5]**Marek Fisz,*Probability theory and mathematical statistics*, Third edition. Authorized translation from the Polish. Translated by R. Bartoszynski, John Wiley & Sons, Inc., New York-London, 1963. MR**0164358****[6]**Harald Cramér,*Mathematical Methods of Statistics*, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR**0016588****[7]**L. R. Ford Jr. and D. R. Fulkerson,*Flows in networks*, Princeton University Press, Princeton, N.J., 1962. MR**0159700****[8]**F. R. Gantmacher,*The theory of matrices*, Vol. I, Chelsea, New York, 1960**[9]**Shanti S. Gupta,*Probability integrals of multivariate normal and multivariate 𝑡*, Ann. Math. Statist.**34**(1963), 792–828. MR**0152068**, https://doi.org/10.1214/aoms/1177704004**[10]**Charles E. Clark,*The greatest of a finite set of random variables*, Operations Res.**9**(1961), 145–162. MR**0125604****[11]**E. L. Lehmann,*Testing statistical hypotheses*, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1959. MR**0107933**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
94.10

Retrieve articles in all journals with MSC: 94.10

Additional Information

DOI:
https://doi.org/10.1090/qam/233616

Article copyright:
© Copyright 1968
American Mathematical Society