Utility maximization for bandwidth allocation in peer-to-peer file-sharing networks

Shiyong Li; Wei Sun; Quan-Lin Li

doi:10.3934/jimo.2018194

Article Contents

2020, Volume 16, Issue 3: 1099-1117. Doi: 10.3934/jimo.2018194

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Utility maximization for bandwidth allocation in peer-to-peer file-sharing networks

School of Economics and Management, Yanshan University, Qinhuangdao 066004, China

* Corresponding author: Wei Sun
* Corresponding author: Wei Sun

Received: October 2017

Revised: January 2018

Early access: December 2018

Published: March 2020

The authors were supported in part by the National Natural Science Foundation of China (Nos. 71671159, 71301139 and 71671158), the Humanity and Social Science Foundation of Ministry of Education of China (No. 16YJC630106), the Natural Science Foundation of Hebei Province (Nos. G2018203302 and G2016203236), the project Funded by Hebei Education Department (Nos. BJ2017029 and BJ2016063) and Hebei Talents Program (No. A2017002108)

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Abstract

Peer-to-peer (P2P) networks have been commonly applied into many applications such as distributed storage, cloud computing and social networking. In P2P networks fairness fosters an incentive so as to encourage peers to offer resources (e.g, upload bandwidth) to the networks. In this paper, we consider fair bandwidth allocation of access links in P2P file-sharing networks and develop a coupled network-wide utility maximization model which aims at achieving several kinds of fairness among requesting peers. We provide a meaningful interpretation of the problem of maximizing social welfare and its sub-problems from an economic point of view. The coupled optimization problem is difficult to resolve in a distributed way because of its non-strict convexity and non-separation. We apply a modified successive approximation method to investigate the coupled problem and propose a distributed bandwidth allocation scheme to solve the approximation problems. Then, we investigate the convergence of the scheme by mathematical analysis and evaluate the performance through numerical examples, which validate that the scheme can achieve the global optimum within reasonable iterations.

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Mathematics Subject Classification: Primary: 68M10, 68M20; Secondary: 90C30.

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Figure 1. The resource allocation algorithm

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Figure 2. Total number of iterations for the convergence of the proposed algorithm for coupled model

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Figure 3. Performance of the resource allocation algorithm: fully coupled

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Figure 4. Performance of the resource allocation algorithm: uncoupled

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Figure 5. Performance of the resource allocation algorithm: half coupled

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Figure 6. Optimal resource allocation obtained by the algorithm in three cases and LINGO

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Figure 7. Optimal resource allocation for different fairness concepts

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Figure 8. Aggregated utility of P2P networks with different number of peers

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Table 1. The optimum for the resource allocation model: fully coupled

variable	$ x_{11}^* $	$ x_{21}^* $	$ x_{12}^* $	$ x_{22}^* $	$ x_{13}^* $	$ x_{23}^* $
algorithm	5.4523	9.2144	3.8215	6.1785	2.7262	4.6072
LINGO	6.0114	8.6553	2.6028	7.3972	3.3859	3.9475

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Table 2. The optimum for the resource allocation model: uncoupled

variable	$ x_{11}^* $	$ x_{21}^* $	$ x_{12}^* $	$ x_{22}^* $	$ x_{13}^* $	$ x_{23}^* $
algorithm	5.4534	9.2143	3.8233	6.1791	2.7272	4.6071
LINGO	5.4524	9.2143	3.8214	6.1786	2.7262	4.6071

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Table 3. The optimum for the resource allocation model: half coupled

variable	$ x_{11}^* $	$ x_{21}^* $	$ x_{12}^* $	$ x_{22}^* $	$ x_{13}^* $	$ x_{23}^* $
algorithm	5.4516	9.2151	3.8227	6.1773	2.7248	4.6096
LINGO	5.4524	9.2143	3.8214	6.1786	2.7262	4.6071

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