Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Minimum cost flows over time without intermediate storage
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Uniform resource networks I. Complete graphs
Automation and Remote Control
Asymmetric resource networks. II. Flows for large resources and their stabilization
Automation and Remote Control
Control of limit states in absorbing resource networks
Automation and Remote Control
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We consider dynamic resource allocation processes in two-sided asymmetrical resource networks with loops and study their stabilization conditions. We show that for a unit total resource, the resource reallocation process defines a regular Markov chain, and the limit state vector corresponds to the vector of limit probabilities and is an eigenvector of the stochastic matrix corresponding to the capacity matrix. We show that (a) for a resource not exceeding some threshold value, the limit state vector also exists, is unique, and is proportional to the limit probability vector; (b) for any connected network, the threshold value of total resource exists and is unique.