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Some limit theorems for a class of network problems as related to finite Markov chains

Published online by Cambridge University Press:  14 July 2016

Masao Nakamura
Masao Nakamura*
Affiliation:
University of Alberta, Edmonton
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Abstract

This paper is concerned with a class of dynamic network flow problems in which the amount of flow leaving node i in one time period for node j is the fraction pij of the total amount of flow which arrived at node i during the previous time period. The fraction pij whose sum over j equals unity may be interpreted as the transition probability of a finite Markov chain in that the unit flow in state i will move to state j with probability pij during the next period of time. The conservation equations for this class of flows are derived, and the limiting behavior of the flows in the network as related to the properties of the fractions Pij are discussed.

Keywords

DYNAMIC NETWORK FLOWFINITE MARKOV CHAINTRANSITION PROBABILITIESNON-NEGATIVE MATRICESAPERIODICITYIRREDUCIBILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 94 - 101
Copyright
Copyright © Applied Probability Trust 1974 

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References

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