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:
[1]

M. Analoui and M. H. Rezvani, Microeconomics-based resource allocation in overlay networks by using non-strategic behavior modeling, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 493-508. doi: 10.1016/j.cnsns.2010.04.005. Google Scholar

[2]

E. Antal and T. Vinkó, Modeling max-min fair bandwidth allocation in BitTorrent communities, Computational Optimization and Applications, 66 (2017), 1-18. doi: 10.1007/s10589-016-9866-5. Google Scholar

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D. P. Bertsekas, Nonlinear Programming, Second edition. Athena Scientific Optimization and Computation Series. Athena Scientific, Belmont, MA, 1999. Google Scholar

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M. ChenM. PonecS. SenguptaJ. Li and P. A. Chou, Utility maximization in peer-to-peer systems with applications to video conferencing, IEEE/ACM Transactions on Networking, 20 (2012), 1681-1694. Google Scholar

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M. ChiangS. H. LowA. R. Calderbank and J. C. Doyle, Layering as optimization decomposition: A mathematical theory of network architectures, Proceedings of the IEEE, 95 (2007), 255-312. Google Scholar

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M. ChiangC. W. TanD. P. PalomarD. O'Neill and D. Julian, Power control by geometric programming, IEEE Transactions on Wireless Communications, 6 (2007), 2640-2650. Google Scholar

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K. Eger and U. Killat, Fair resource allocation in peer-to-peer networks (extended version), Computer Communications, 30 (2007), 3046-3054. Google Scholar

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A. S. ElmaghrabyA. KumarM. M. Kantardzic and M. G. Mostafa, A scalable pricing model for bandwidth allocation, Electronic Commerce Research, 5 (2005), 203-227. Google Scholar

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S. JinY. ZhaoW. Yue and L. Chen., Performance analysis of a P2P storage system with a lazy replica repair policy, Journal of Industrial and Management Optimization, 10 (2014), 151-166. doi: 10.3934/jimo.2014.10.151. Google Scholar

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F. P. KellyA. Maulloo and D. Tan, Rate control in communication networks: Shadow prices, proportional fairness and stability, Journal of the Operational Research Society, 49 (1998), 237-252. Google Scholar

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I. Koutsopoulos and G. Iosifidis, A framework for distributed bandwidth allocation in peer-to-peer networks, Performance Evaluation, 67 (2010), 285-298. Google Scholar

[12]

C. KumarK. Altinkemer and P. De, A mechanism for pricing and resource allocation in peer-to-peer networks, Electronic Commerce Research and Applications, 10 (2011), 26-37. Google Scholar

[13]

S. Li and W. Sun, A mechanism for resource pricing and fairness in peer-to-peer networks, Electronic Commerce Research, 16 (2016), 425-451. Google Scholar

[14]

S. LiW. Sun and C. Hua, Fair resource allocation and stability for communication networks with multipath routing, International Journal of Systems Science, 45 (2014), 2342-2353. doi: 10.1080/00207721.2013.769073. Google Scholar

[15]

S. LiW. Sun and N. Tian, Resource allocation for multi-class services in multipath networks, Performance Evaluation, 92 (2015), 1-23. Google Scholar

[16]

Z. Li and Q. Liao, Network pricing: Can both ISP and P2P benefit?, International Journal of Network Management, 24 (2014), 433-449. Google Scholar

[17]

F. LinX. ZhouD. HuangY. Chen and J. Yuan, Hierarchical name system based on hybrid P2P for multimedia networks, Telecommunication Systems, 59 (2015), 393-400. Google Scholar

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P. LinP.-C. Chung and Y. Fang, P2P-iSN: A peer-to-peer architecture for heterogeneous social networks, IEEE Network, 28 (2014), 56-64. Google Scholar

[19]

B. R. Marks and G. P. Wright, A general inner approximation algorithm for nonconvex mathematical programs, Operations Research, 26 (1978), 681-683. doi: 10.1287/opre.26.4.681. Google Scholar

[20]

M. J. Neely and L. Golubchik, Utility optimization for dynamic peer-to-peer networks with tit-for-tat constraints, IEEE INFOCOM, 2011, 1458-1466.Google Scholar

[21]

H. Nishida and T. Nguyen, A global contribution approach to maintain fairness in P2P networks, IEEE Transactions on Parallel and Distributed Systems, 21 (2010), 812-826. Google Scholar

[22]

B. QureshiG. Min and D. Kouvatsos, A distributed reputation and trust management scheme for mobile peer-to-peer networks, Computer Communications, 35 (2012), 608-618. Google Scholar

[23]

S. RhoH. ChangS. Kim and Y. S. Lee, An efficient peer-to-peer and distributed scheduling for cloud and grid computing, Peer-to-Peer Networking and Applications, 8 (2014), 863-871. Google Scholar

[24]

I. Rubin and R. Zhang, Max-min utility fair flow management for networks with route diversity, International Journal of Network Management, 20 (2010), 361-381. Google Scholar

[25]

A. Satsiou and L. Tassiulas, Reputation-based resource allocation in P2P systems of rational users, IEEE Transactions on Parallel and Distributed Systems, 21 (2010), 466-479. Google Scholar

[26]

S. Shakkottai and R. Srikant, Network optimization and control, Foundations and Trends in Networking, 2 (2007), 271-379. Google Scholar

[27]

F. SongD. HuangH. ZhouH. Zhang and I. You, An optimization-based scheme for efficient virtual machine placement, International Journal of Parallel Programming, 42 (2014), 853-872. Google Scholar

[28]

F. SongY. ZhangZ. AnH. Zhou and I. You, The correlation study for parameters in four tuples, International Journal of Ad Hoc and Ubiquitous Computing, 19 (2015), 38-49. Google Scholar

[29]

N. H. Tran and C. S. Hong, Joint rate and power control in wireless network: A novel successive approximations method, IEEE Communications Letters, 14 (2010), 872-874. Google Scholar

[30]

P. L. VoT. A. LeS. LeeC. S. HongB. Kim and H. Song, MReno: A practical multipath congestion control for communication networks, Computing, 96 (2014), 189-205. doi: 10.1007/s00607-013-0341-1. Google Scholar

[31]

P. L. VoT. A. LeS. LeeC. S. HongB. Kim and H. Song, Multi-path utility maximization and multi-path TCP design, Journal of Parallel and Distributed Computing, 74 (2014), 1848-1857. Google Scholar

[32]

K. WangH. YinW. Quan and G. Min, Enabling collaborative edge computing for software defined vehicular networks, IEEE Network, 32 (2018), 112-117. Google Scholar

[33]

H. YanD. GaoW. SuC. H. FohH. Zhang and A. V. Vasilakos, Caching strategy based on hierarchical cluster for named data networking, IEEE Access, 5 (2017), 8433-8443. Google Scholar

[34]

K. Zhang and N. Antonopoulos, A novel bartering exchange ring based incentive mechanism for peer-to-peer systems, Future Generation Computer Systems, 29 (2013), 361-369. Google Scholar

[35]

Y. ZhengF. LinY. Yang and T. Gan, Adaptive resource scheduling mechanism in P2P file sharing system, Peer-to-Peer Networking and Applications, 9 (2016), 1089-1100. Google Scholar

show all references

References:
[1]

M. Analoui and M. H. Rezvani, Microeconomics-based resource allocation in overlay networks by using non-strategic behavior modeling, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 493-508. doi: 10.1016/j.cnsns.2010.04.005. Google Scholar

[2]

E. Antal and T. Vinkó, Modeling max-min fair bandwidth allocation in BitTorrent communities, Computational Optimization and Applications, 66 (2017), 1-18. doi: 10.1007/s10589-016-9866-5. Google Scholar

[3]

D. P. Bertsekas, Nonlinear Programming, Second edition. Athena Scientific Optimization and Computation Series. Athena Scientific, Belmont, MA, 1999. Google Scholar

[4]

M. ChenM. PonecS. SenguptaJ. Li and P. A. Chou, Utility maximization in peer-to-peer systems with applications to video conferencing, IEEE/ACM Transactions on Networking, 20 (2012), 1681-1694. Google Scholar

[5]

M. ChiangS. H. LowA. R. Calderbank and J. C. Doyle, Layering as optimization decomposition: A mathematical theory of network architectures, Proceedings of the IEEE, 95 (2007), 255-312. Google Scholar

[6]

M. ChiangC. W. TanD. P. PalomarD. O'Neill and D. Julian, Power control by geometric programming, IEEE Transactions on Wireless Communications, 6 (2007), 2640-2650. Google Scholar

[7]

K. Eger and U. Killat, Fair resource allocation in peer-to-peer networks (extended version), Computer Communications, 30 (2007), 3046-3054. Google Scholar

[8]

A. S. ElmaghrabyA. KumarM. M. Kantardzic and M. G. Mostafa, A scalable pricing model for bandwidth allocation, Electronic Commerce Research, 5 (2005), 203-227. Google Scholar

[9]

S. JinY. ZhaoW. Yue and L. Chen., Performance analysis of a P2P storage system with a lazy replica repair policy, Journal of Industrial and Management Optimization, 10 (2014), 151-166. doi: 10.3934/jimo.2014.10.151. Google Scholar

[10]

F. P. KellyA. Maulloo and D. Tan, Rate control in communication networks: Shadow prices, proportional fairness and stability, Journal of the Operational Research Society, 49 (1998), 237-252. Google Scholar

[11]

I. Koutsopoulos and G. Iosifidis, A framework for distributed bandwidth allocation in peer-to-peer networks, Performance Evaluation, 67 (2010), 285-298. Google Scholar

[12]

C. KumarK. Altinkemer and P. De, A mechanism for pricing and resource allocation in peer-to-peer networks, Electronic Commerce Research and Applications, 10 (2011), 26-37. Google Scholar

[13]

S. Li and W. Sun, A mechanism for resource pricing and fairness in peer-to-peer networks, Electronic Commerce Research, 16 (2016), 425-451. Google Scholar

[14]

S. LiW. Sun and C. Hua, Fair resource allocation and stability for communication networks with multipath routing, International Journal of Systems Science, 45 (2014), 2342-2353. doi: 10.1080/00207721.2013.769073. Google Scholar

[15]

S. LiW. Sun and N. Tian, Resource allocation for multi-class services in multipath networks, Performance Evaluation, 92 (2015), 1-23. Google Scholar

[16]

Z. Li and Q. Liao, Network pricing: Can both ISP and P2P benefit?, International Journal of Network Management, 24 (2014), 433-449. Google Scholar

[17]

F. LinX. ZhouD. HuangY. Chen and J. Yuan, Hierarchical name system based on hybrid P2P for multimedia networks, Telecommunication Systems, 59 (2015), 393-400. Google Scholar

[18]

P. LinP.-C. Chung and Y. Fang, P2P-iSN: A peer-to-peer architecture for heterogeneous social networks, IEEE Network, 28 (2014), 56-64. Google Scholar

[19]

B. R. Marks and G. P. Wright, A general inner approximation algorithm for nonconvex mathematical programs, Operations Research, 26 (1978), 681-683. doi: 10.1287/opre.26.4.681. Google Scholar

[20]

M. J. Neely and L. Golubchik, Utility optimization for dynamic peer-to-peer networks with tit-for-tat constraints, IEEE INFOCOM, 2011, 1458-1466.Google Scholar

[21]

H. Nishida and T. Nguyen, A global contribution approach to maintain fairness in P2P networks, IEEE Transactions on Parallel and Distributed Systems, 21 (2010), 812-826. Google Scholar

[22]

B. QureshiG. Min and D. Kouvatsos, A distributed reputation and trust management scheme for mobile peer-to-peer networks, Computer Communications, 35 (2012), 608-618. Google Scholar

[23]

S. RhoH. ChangS. Kim and Y. S. Lee, An efficient peer-to-peer and distributed scheduling for cloud and grid computing, Peer-to-Peer Networking and Applications, 8 (2014), 863-871. Google Scholar

[24]

I. Rubin and R. Zhang, Max-min utility fair flow management for networks with route diversity, International Journal of Network Management, 20 (2010), 361-381. Google Scholar

[25]

A. Satsiou and L. Tassiulas, Reputation-based resource allocation in P2P systems of rational users, IEEE Transactions on Parallel and Distributed Systems, 21 (2010), 466-479. Google Scholar

[26]

S. Shakkottai and R. Srikant, Network optimization and control, Foundations and Trends in Networking, 2 (2007), 271-379. Google Scholar

[27]

F. SongD. HuangH. ZhouH. Zhang and I. You, An optimization-based scheme for efficient virtual machine placement, International Journal of Parallel Programming, 42 (2014), 853-872. Google Scholar

[28]

F. SongY. ZhangZ. AnH. Zhou and I. You, The correlation study for parameters in four tuples, International Journal of Ad Hoc and Ubiquitous Computing, 19 (2015), 38-49. Google Scholar

[29]

N. H. Tran and C. S. Hong, Joint rate and power control in wireless network: A novel successive approximations method, IEEE Communications Letters, 14 (2010), 872-874. Google Scholar

[30]

P. L. VoT. A. LeS. LeeC. S. HongB. Kim and H. Song, MReno: A practical multipath congestion control for communication networks, Computing, 96 (2014), 189-205. doi: 10.1007/s00607-013-0341-1. Google Scholar

[31]

P. L. VoT. A. LeS. LeeC. S. HongB. Kim and H. Song, Multi-path utility maximization and multi-path TCP design, Journal of Parallel and Distributed Computing, 74 (2014), 1848-1857. Google Scholar

[32]

K. WangH. YinW. Quan and G. Min, Enabling collaborative edge computing for software defined vehicular networks, IEEE Network, 32 (2018), 112-117. Google Scholar

[33]

H. YanD. GaoW. SuC. H. FohH. Zhang and A. V. Vasilakos, Caching strategy based on hierarchical cluster for named data networking, IEEE Access, 5 (2017), 8433-8443. Google Scholar

[34]

K. Zhang and N. Antonopoulos, A novel bartering exchange ring based incentive mechanism for peer-to-peer systems, Future Generation Computer Systems, 29 (2013), 361-369. Google Scholar

[35]

Y. ZhengF. LinY. Yang and T. Gan, Adaptive resource scheduling mechanism in P2P file sharing system, Peer-to-Peer Networking and Applications, 9 (2016), 1089-1100. Google Scholar

Figure 1.  The resource allocation algorithm
Figure 2.  Total number of iterations for the convergence of the proposed algorithm for coupled model
Figure 3.  Performance of the resource allocation algorithm: fully coupled
Figure 4.  Performance of the resource allocation algorithm: uncoupled
Figure 5.  Performance of the resource allocation algorithm: half coupled
Figure 6.  Optimal resource allocation obtained by the algorithm in three cases and LINGO
Figure 7.  Optimal resource allocation for different fairness concepts
Figure 8.  Aggregated utility of P2P networks with different number of peers
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
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
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
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
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
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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