Abstract
The asymptotic behavior of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. For this model, each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes on its route. In this situation Graham and Robert [6] has shown that the invariant distributions are in a one-to-one correspondence with the solutions of a fixed point equation in a finite dimensional space. The purpose of this paper is to investigate the problem of uniqueness of the equilibrium of these networks, i.e., the uniqueness of the solutions of the associated fixed point equation. Uniqueness results of such solutions are proved for different topologies: rings, trees and a linear network and with various configurations for routes through nodes.
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Graham, C., Robert, P., Verloop, M. (2009). Stability Properties of Networks with Interacting TCP Flows. In: Núñez-Queija, R., Resing, J. (eds) Network Control and Optimization. NET-COOP 2009. Lecture Notes in Computer Science, vol 5894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10406-0_1
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DOI: https://doi.org/10.1007/978-3-642-10406-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10405-3
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