New Discoveries of Domination Between Traffic Matrices

In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominates D2. Let u（D） be the set of all the traffic matrices that are dominated by the traffic...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2017-07, Vol.33 (3), p.561-566
Main Authors: Liu, Peng-fei, Yang, Wen-guo, Guo, Tian-de
Format: Article
Language:English
Subjects:
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Traffic flow
交通
流量矩阵
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Summary:In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominates D2. Let u（D） be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that u （ D∞） and u （D ∈） are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Fhrthermore, the results are the generalized to integral flows.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-017-0636-7