# Completely Uncoupled Algorithms for Network Utility Maximization

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### Cites methods from "Completely Uncoupled Algorithms for..."

...Theoretically, the network resource scheduling optimization was modeled as a NUM problem [9, 11, 12]....

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### Cites background or methods from "Completely Uncoupled Algorithms for..."

...We conclude by noting that, with modifications as considered in this paper, we could extend the subgradient algorithm in [22] to a state based model as well....

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...In our earlier work [22], we have presented a completely uncoupled subgradient algorithm for maximizing concave utilities....

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##### References

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^{1}, University of Cassino

^{2}, Macquarie University

^{3}, Pompeu Fabra University

^{4}, Huawei

^{5}, Samsung

^{6}

7,139 citations

### "Completely Uncoupled Algorithms for..." refers background in this paper

...With the advances in 5G wireless systems, it is predicted that there will be a phenomenal increase in the number of access points [2]....

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4,070 citations

### "Completely Uncoupled Algorithms for..." refers methods in this paper

...f the joint action proﬁle. A completely uncoupled algorithm to reach efﬁcient Nash equilibrium was proposed by Pradelski et al in [4]. The algorithm was based on the theory of perturbed Markov chains [29],[30]. With similar ideas, Marden et al proposed algorithms to achieve maximum sum payoff in [5]. These algorithms were adapted to wireless networks in [31],[32]. In [33], Borowski et al proposed dist...

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...is of G-NUM In this section, we discuss the optimality of G-NUM. We characterize the performance of G-NUM as t!1and !0. To analyze the performance of G-NUM, we use tools from perturbed Markov chains [29], [30]. We ﬁrst show that GNUM induces a perturbed Markov chain (perturbed by ). In Theorem 1, we show that the stochastically stable states (See Deﬁnition 2) of the Markov chain induced by G-NUM are...

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...terest. VIII. APPENDIX A. Proof of Theorem 1: To prove theorem 1, we need to characterize the stationary distribution of X (t) for small . For such a characterization, we shall use the results from [29],[30] on perturbed Markov chains. Let P (x;y) denote the transition probability of the Markov chain X from state xto state y. Consider the directed graph Gwith the states of the Markov chain as vert...

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3,018 citations

### "Completely Uncoupled Algorithms for..." refers background in this paper

...Related Literature Tassiulas and Ephremides proposed the Max-weight algorithm in [7]....

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...The main drawback of the Max-weight algorithm, used in [7]–[9], is its complexity and centralized nature....

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...The Max-weight algorithm can stabilize any arrival rate within the rate region [7]....

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