Load distribution performance of super-node based peer-to-peer communication networks: A nonstationary Markov chain approach

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2011, 1(4): 593-610. doi: 10.3934/naco.2011.1.593

Load distribution performance of super-node based peer-to-peer communication networks: A nonstationary Markov chain approach

Kazuhiko Kuraya ^1, , Hiroyuki Masuyama ^2, and Shoji Kasahara ^2,

1.	Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
2.	Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501

Received May 2011 Revised August 2011 Published November 2011

Abstract
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Voice over Internet protocol (VoIP) services using peer-to-peer (P2P) technology have become popular in recent years. In P2P-based VoIP networks such as Skype and P2P session initiation protocol (P2PSIP), super nodes are chosen from among all ordinary end-user nodes and handle particular tasks such as the management of user information, call establishment, and traffic relay. Future communication networks based on P2P technology must support a huge number of user nodes. A fundamental analysis of the load distribution in decentralized user-information management is needed to develop efficient and robust communication networks. In this paper, we analyze the performance of the P2P-based dynamic load distribution. In our analytical model, new nodes join the network according to a nonstationary Poisson process, and the stochastic behavior of the number of online nodes is analyzed approximately with an M($t$)/M/$\infty$ queue. We focus on two performance measures that significantly affect the quality of service (QoS) provided to the users: the churn rate and the load of super nodes. Numerical examples show that the performance of the P2P-based VoIP networks is sensitive to the sojourn time of super nodes and the maximum number of nodes managed by a super node.

Keywords: nonstationary queue, VoIP., nonstationary Poisson process, Decentralized user information management system, nonstationary Markov chain, online node process, QoS, P2P.

Mathematics Subject Classification: Primary: 68M20; Secondary: 60K25, 68M2.

Citation: Kazuhiko Kuraya, Hiroyuki Masuyama, Shoji Kasahara. Load distribution performance of super-node based peer-to-peer communication networks: A nonstationary Markov chain approach. Numerical Algebra, Control and Optimization, 2011, 1 (4) : 593-610. doi: 10.3934/naco.2011.1.593

References:

[1]	K. A. Alnowibet and H. Perros, The nonstationary loss queue: a survey, in "Modelling of Computer Systems and Networks"(ed. J. Barria), Imperial College Press, (2005), 105-125.
[2]	S. A. Baset and H. G. Schulzrinne, An analysis of the Skype peer-to-peer Internet telephony protocol, Proceedings of the 25th International Conference on Computer Communications, IEEE INFOCOM, (2006), 1-11.
[3]	D. A. Bryan, B. B. Lowekamp and C. Jennings, SOSIMPLE: a serverless, standards-based, P2P SIP communication system, Proceedings of International Workshop on Advanced Workshop and Algorithms for Internet Delivery and Applications, AAA-IDEA 2005, 42-49.
[4]	G. Caizzone, A. Corghi, P. Giacomazzi and M. Nonnoi, Analysis of the scalability of the overlay Skype system, Proceedings of the IEEE International Conference on Communications, (2008), 5652-5658.
[5]	K. Chen, C. Huang, P. Huang and C. Lei, Quantifying Skype user satisfaction, Proceedings of ACM SIGCOMM, (2006), 399-410.
[6]	S. G. Eick, W. A. Massey and W. Whitt, M$_t$/G/$\infty$ queues with sinusoidal arrival rates, Management Science, 39 (1993), 241-252. doi: 10.1287/mnsc.39.2.241.
[7]	Z. Ge, D. R. Figueiredo, S. Jaiswal, J. Kurose and D. Towsley, Modeling peer-peer file sharing systems, Proceedings of the 22th International Conference on Computer Communications, IEEE INFOCOM, (2003), 2188-2198.
[8]	L. Green, P. Kolesar and A. Svoronos, Some effects of nonstationarity on multiserver Markovian queueing systems, Operations Research, 39 (1991), 502-511. doi: 10.1287/opre.39.3.502.
[9]	S. Guha, N. Daswani and R. Jain, An experimental study of the Skype peer-to-peer VoIP system, Proceedings of the 5th International Workshop on Peer-to-Peer Systems, (2006), 1-6.
[10]	D. P. Heyman and W. Whitt, The asymptotic behavior of queues with time-varying arrival rates, Journal of Applied Probability, 21 (1984), 143-156. doi: 10.2307/3213672.
[11]	D. L. Jagerman, Nonstationary blocking in telephone traffic, The Bell System Technical Journal, 54 (1975), 625-661.
[12]	V. G. Kulkarni, "Modeling and Analysis of Stochastic Systems," Chapman $ & $ Hall, 1995.
[13]	K. Kuraya, H. Masuyama, S. Kasahara and Y. Takahashi, Performance analysis of decentralized user information management system for peer-to-peer real-time communication services, Proceedings of the 6th Symposium on Communication Systems, Networks and Digital Signal Processing, (2008), 520-524. doi: 10.1109/CSNDSP.2008.4610821.
[14]	L. Le and G. Kuo, Hierarchical and breathing peer-to-peer SIP system, Proceedings of the IEEE International Conference on Communications, (2007), 1887-1892. doi: 10.1109/ICC.2007.314.
[15]	P. A. W. Lewis and G. S. Shedler, Simulation of nonhomogeneous Poisson processes by thinning, Naval Research Logistics Quarterly, 26 (1979), 403-413. doi: 10.1002/nav.3800260304.
[16]	W. A. Massey and W. Whitt, Stationary-process approximation for the nonstationary Erlang loss model, Operations Research, 44 (1996), 976-983. doi: 10.1287/opre.44.6.976.
[17]	J. Rosenberg, R. Mahy and P. Matthews, Traversal using relay around NAT (TURN): relay extensions to session traversal utilities for NAT (STUN), IETF Internet draft, Work in progress, 2008.
[18]	J. Rosenberg, R. Mahy, P. Matthews and D. Wing, Session traversal utilities for NAT (STUN), IETF RFC (2008), http://www.ietf.org/rfc/rfc5389.txt.
[19]	S. Saroiu, P. K. Gummadi and S. D. Gribble, A measurement study of peer-to-peer file sharing systems, Technical Report, UW-CSE-01-06-02, University of Washington, 2001.
[20]	H. Schulzrinne and J. Rosenberg, The session initiation protocol: Internet-centric signaling, IEEE Communications Magazine, 38 (2000), 134-141. doi: 10.1109/35.874980.
[21]	K. Singh and H. Schulzrinne, SIPpeer: a session initiation protocol (SIP)-based peer-to-peer Internet telephony client adaptor, http://www1.cs.columbia.edu/ kns10/publication/sip-p2p-design.pdf.
[22]	K. Singh and H. Schulzrinne, Peer-to-peer Internet telephony using SIP, Proceedings of ACM NOSSDAV, (2005), 63-68.
[23]	X. Yang and G. de Veciana，, Performance of peer-to-peer networks: service capacity and role of resource sharing policies, Performance Evaluation, 63 (2006), 175-194. doi: 10.1016/j.peva.2005.01.005.
[24]	, P2PSIP working group, http://tools.ietf.org/wg/p2psip/.
[25]	, Skype, http://www.skype.com/.
[26]	, Skype statistics, http://share.skype.com/stats_rss.xml.

show all references

References:

[1]	K. A. Alnowibet and H. Perros, The nonstationary loss queue: a survey, in "Modelling of Computer Systems and Networks"(ed. J. Barria), Imperial College Press, (2005), 105-125.
[2]	S. A. Baset and H. G. Schulzrinne, An analysis of the Skype peer-to-peer Internet telephony protocol, Proceedings of the 25th International Conference on Computer Communications, IEEE INFOCOM, (2006), 1-11.
[3]	D. A. Bryan, B. B. Lowekamp and C. Jennings, SOSIMPLE: a serverless, standards-based, P2P SIP communication system, Proceedings of International Workshop on Advanced Workshop and Algorithms for Internet Delivery and Applications, AAA-IDEA 2005, 42-49.
[4]	G. Caizzone, A. Corghi, P. Giacomazzi and M. Nonnoi, Analysis of the scalability of the overlay Skype system, Proceedings of the IEEE International Conference on Communications, (2008), 5652-5658.
[5]	K. Chen, C. Huang, P. Huang and C. Lei, Quantifying Skype user satisfaction, Proceedings of ACM SIGCOMM, (2006), 399-410.
[6]	S. G. Eick, W. A. Massey and W. Whitt, M$_t$/G/$\infty$ queues with sinusoidal arrival rates, Management Science, 39 (1993), 241-252. doi: 10.1287/mnsc.39.2.241.
[7]	Z. Ge, D. R. Figueiredo, S. Jaiswal, J. Kurose and D. Towsley, Modeling peer-peer file sharing systems, Proceedings of the 22th International Conference on Computer Communications, IEEE INFOCOM, (2003), 2188-2198.
[8]	L. Green, P. Kolesar and A. Svoronos, Some effects of nonstationarity on multiserver Markovian queueing systems, Operations Research, 39 (1991), 502-511. doi: 10.1287/opre.39.3.502.
[9]	S. Guha, N. Daswani and R. Jain, An experimental study of the Skype peer-to-peer VoIP system, Proceedings of the 5th International Workshop on Peer-to-Peer Systems, (2006), 1-6.
[10]	D. P. Heyman and W. Whitt, The asymptotic behavior of queues with time-varying arrival rates, Journal of Applied Probability, 21 (1984), 143-156. doi: 10.2307/3213672.
[11]	D. L. Jagerman, Nonstationary blocking in telephone traffic, The Bell System Technical Journal, 54 (1975), 625-661.
[12]	V. G. Kulkarni, "Modeling and Analysis of Stochastic Systems," Chapman $ & $ Hall, 1995.
[13]	K. Kuraya, H. Masuyama, S. Kasahara and Y. Takahashi, Performance analysis of decentralized user information management system for peer-to-peer real-time communication services, Proceedings of the 6th Symposium on Communication Systems, Networks and Digital Signal Processing, (2008), 520-524. doi: 10.1109/CSNDSP.2008.4610821.
[14]	L. Le and G. Kuo, Hierarchical and breathing peer-to-peer SIP system, Proceedings of the IEEE International Conference on Communications, (2007), 1887-1892. doi: 10.1109/ICC.2007.314.
[15]	P. A. W. Lewis and G. S. Shedler, Simulation of nonhomogeneous Poisson processes by thinning, Naval Research Logistics Quarterly, 26 (1979), 403-413. doi: 10.1002/nav.3800260304.
[16]	W. A. Massey and W. Whitt, Stationary-process approximation for the nonstationary Erlang loss model, Operations Research, 44 (1996), 976-983. doi: 10.1287/opre.44.6.976.
[17]	J. Rosenberg, R. Mahy and P. Matthews, Traversal using relay around NAT (TURN): relay extensions to session traversal utilities for NAT (STUN), IETF Internet draft, Work in progress, 2008.
[18]	J. Rosenberg, R. Mahy, P. Matthews and D. Wing, Session traversal utilities for NAT (STUN), IETF RFC (2008), http://www.ietf.org/rfc/rfc5389.txt.
[19]	S. Saroiu, P. K. Gummadi and S. D. Gribble, A measurement study of peer-to-peer file sharing systems, Technical Report, UW-CSE-01-06-02, University of Washington, 2001.
[20]	H. Schulzrinne and J. Rosenberg, The session initiation protocol: Internet-centric signaling, IEEE Communications Magazine, 38 (2000), 134-141. doi: 10.1109/35.874980.
[21]	K. Singh and H. Schulzrinne, SIPpeer: a session initiation protocol (SIP)-based peer-to-peer Internet telephony client adaptor, http://www1.cs.columbia.edu/ kns10/publication/sip-p2p-design.pdf.
[22]	K. Singh and H. Schulzrinne, Peer-to-peer Internet telephony using SIP, Proceedings of ACM NOSSDAV, (2005), 63-68.
[23]	X. Yang and G. de Veciana，, Performance of peer-to-peer networks: service capacity and role of resource sharing policies, Performance Evaluation, 63 (2006), 175-194. doi: 10.1016/j.peva.2005.01.005.
[24]	, P2PSIP working group, http://tools.ietf.org/wg/p2psip/.
[25]	, Skype, http://www.skype.com/.
[26]	, Skype statistics, http://share.skype.com/stats_rss.xml.

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