Premium
Maximum flow in probabilistic communication networks
Author(s) -
Nawathe S. P.,
Rao B. V.
Publication year - 1980
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490080209
Subject(s) - monte carlo method , probabilistic logic , mathematical optimization , flow (mathematics) , random variable , flow network , limit (mathematics) , simple (philosophy) , moment (physics) , computer science , variance (accounting) , central limit theorem , mathematics , distribution (mathematics) , topology (electrical circuits) , algorithm , statistics , artificial intelligence , combinatorics , physics , mathematical analysis , philosophy , geometry , accounting , epistemology , classical mechanics , business
The purpose of this paper is to provide a general approach for the problems of analysis and synthesis of probabilistic communication networks. The flows in the branches of a network may be interdependent random variables having any arbitrary distribution. A simple technique, based on the theory of best linear prediction, enables Monte Carlo simulation of such a network. The simulation results suggest that the distribution of the maximum flow (that can be established in the network) can be approximated by a normal distribution despite the inapplicability of the central limit theorem. The results of Monte Carlo simulation are consistent with those obtained through an alternative analytical procedure. The synthesis problem considered in this paper is that of finding the branch capacities of a network so that a given demand for flow (specified in terms of its mean and variance), between a pair of vertices of interest, is satisfied. A direct search method (to find out the optimal branch capacity vector) enables simultaneous consideration of the first two moments of the maximum flow as against the existing ones which consider only the first moment.