Generalizations of bounds on the index of convergence to weighted digraphs

Glenn Merlet 1 Thomas Nowak 2 Hans Schneider 3 Sergei Sergeev 4
2 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Sequences of maximum-weight walks of a growing length in weighted digraphs have many applications in manu-facturing and transportation systems, as they encode important performance parameters. It is well-known that they eventually enter a periodic regime if the digraph is strongly connected. The length of their transient phase depends, in general, both on the size of digraph and on the magnitude of the weights. In this paper, we show that certain bounds on the transients of unweighted digraphs, such as the bounds of Wielandt, Dulmage-Mendelsohn, Schwarz, Kim and Gregory-Kirkland-Pullman, remain true for critical nodes in weighted digraphs.
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Glenn Merlet, Thomas Nowak, Hans Schneider, Sergei Sergeev. Generalizations of bounds on the index of convergence to weighted digraphs. IEEE Conference on Decision and Control, Dec 2014, Los Angeles, United States. ⟨10.1109/CDC.2014.7039627⟩. ⟨hal-01107293⟩

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