# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2018194

## 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

Received  October 2017 Revised  January 2018 Published  December 2018

Fund Project: 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)

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.

Citation: Shiyong Li, Wei Sun, Quan-Lin Li. Utility maximization for bandwidth allocation in peer-to-peer file-sharing networks. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018194
##### References:

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##### References:
The resource allocation algorithm
Total number of iterations for the convergence of the proposed algorithm for coupled model
Performance of the resource allocation algorithm: fully coupled
Performance of the resource allocation algorithm: uncoupled
Performance of the resource allocation algorithm: half coupled
Optimal resource allocation obtained by the algorithm in three cases and LINGO
Optimal resource allocation for different fairness concepts
Aggregated utility of P2P networks with different number of peers
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
 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
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
 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
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
 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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