American Institute of Mathematical Sciences

Advanced
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

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 & 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, (2005), 105.   Google Scholar

[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, (2006), 1.   Google Scholar

[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, (2005), 42.   Google Scholar

[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.   Google Scholar

[5]

K. Chen, C. Huang, P. Huang and C. Lei, Quantifying Skype user satisfaction,, Proceedings of ACM SIGCOMM, (2006), 399.   Google Scholar

[6]

S. G. Eick, W. A. Massey and W. Whitt, M$_t$/G/$\infty$ queues with sinusoidal arrival rates,, Management Science, 39 (1993), 241.  doi: 10.1287/mnsc.39.2.241.  Google Scholar

[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, (2003), 2188.   Google Scholar

[8]

L. Green, P. Kolesar and A. Svoronos, Some effects of nonstationarity on multiserver Markovian queueing systems,, Operations Research, 39 (1991), 502.  doi: 10.1287/opre.39.3.502.  Google Scholar

[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.   Google Scholar

[10]

D. P. Heyman and W. Whitt, The asymptotic behavior of queues with time-varying arrival rates,, Journal of Applied Probability, 21 (1984), 143.  doi: 10.2307/3213672.  Google Scholar

[11]

D. L. Jagerman, Nonstationary blocking in telephone traffic,, The Bell System Technical Journal, 54 (1975), 625.   Google Scholar

[12]

V. G. Kulkarni, "Modeling and Analysis of Stochastic Systems,", Chapman $ & $ Hall, (1995).   Google Scholar

[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, (2008), 520.  doi: 10.1109/CSNDSP.2008.4610821.  Google Scholar

[14]

L. Le and G. Kuo, Hierarchical and breathing peer-to-peer SIP system,, Proceedings of the IEEE International Conference on Communications, (2007), 1887.  doi: 10.1109/ICC.2007.314.  Google Scholar

[15]

P. A. W. Lewis and G. S. Shedler, Simulation of nonhomogeneous Poisson processes by thinning,, Naval Research Logistics Quarterly, 26 (1979), 403.  doi: 10.1002/nav.3800260304.  Google Scholar

[16]

W. A. Massey and W. Whitt, Stationary-process approximation for the nonstationary Erlang loss model,, Operations Research, 44 (1996), 976.  doi: 10.1287/opre.44.6.976.  Google Scholar

[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, (2008).   Google Scholar

[18]

J. Rosenberg, R. Mahy, P. Matthews and D. Wing, Session traversal utilities for NAT (STUN),, IETF RFC (2008), (2008).   Google Scholar

[19]

S. Saroiu, P. K. Gummadi and S. D. Gribble, A measurement study of peer-to-peer file sharing systems,, Technical Report, (2001), 01.   Google Scholar

[20]

H. Schulzrinne and J. Rosenberg, The session initiation protocol: Internet-centric signaling,, IEEE Communications Magazine, 38 (2000), 134.  doi: 10.1109/35.874980.  Google Scholar

[21]

K. Singh and H. Schulzrinne, SIPpeer: a session initiation protocol (SIP)-based peer-to-peer Internet telephony client adaptor,, , ().   Google Scholar

[22]

K. Singh and H. Schulzrinne, Peer-to-peer Internet telephony using SIP,, Proceedings of ACM NOSSDAV, (2005), 63.   Google Scholar

[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.  doi: 10.1016/j.peva.2005.01.005.  Google Scholar

[24]

, P2PSIP working group,, , ().   Google Scholar

[25]

, Skype,, , ().   Google Scholar

[26]

, Skype statistics,, , ().   Google Scholar

show all references

References:
[1]

K. A. Alnowibet and H. Perros, The nonstationary loss queue: a survey,, in, (2005), 105.   Google Scholar

[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, (2006), 1.   Google Scholar

[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, (2005), 42.   Google Scholar

[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.   Google Scholar

[5]

K. Chen, C. Huang, P. Huang and C. Lei, Quantifying Skype user satisfaction,, Proceedings of ACM SIGCOMM, (2006), 399.   Google Scholar

[6]

S. G. Eick, W. A. Massey and W. Whitt, M$_t$/G/$\infty$ queues with sinusoidal arrival rates,, Management Science, 39 (1993), 241.  doi: 10.1287/mnsc.39.2.241.  Google Scholar

[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, (2003), 2188.   Google Scholar

[8]

L. Green, P. Kolesar and A. Svoronos, Some effects of nonstationarity on multiserver Markovian queueing systems,, Operations Research, 39 (1991), 502.  doi: 10.1287/opre.39.3.502.  Google Scholar

[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.   Google Scholar

[10]

D. P. Heyman and W. Whitt, The asymptotic behavior of queues with time-varying arrival rates,, Journal of Applied Probability, 21 (1984), 143.  doi: 10.2307/3213672.  Google Scholar

[11]

D. L. Jagerman, Nonstationary blocking in telephone traffic,, The Bell System Technical Journal, 54 (1975), 625.   Google Scholar

[12]

V. G. Kulkarni, "Modeling and Analysis of Stochastic Systems,", Chapman $ & $ Hall, (1995).   Google Scholar

[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, (2008), 520.  doi: 10.1109/CSNDSP.2008.4610821.  Google Scholar

[14]

L. Le and G. Kuo, Hierarchical and breathing peer-to-peer SIP system,, Proceedings of the IEEE International Conference on Communications, (2007), 1887.  doi: 10.1109/ICC.2007.314.  Google Scholar

[15]

P. A. W. Lewis and G. S. Shedler, Simulation of nonhomogeneous Poisson processes by thinning,, Naval Research Logistics Quarterly, 26 (1979), 403.  doi: 10.1002/nav.3800260304.  Google Scholar

[16]

W. A. Massey and W. Whitt, Stationary-process approximation for the nonstationary Erlang loss model,, Operations Research, 44 (1996), 976.  doi: 10.1287/opre.44.6.976.  Google Scholar

[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, (2008).   Google Scholar

[18]

J. Rosenberg, R. Mahy, P. Matthews and D. Wing, Session traversal utilities for NAT (STUN),, IETF RFC (2008), (2008).   Google Scholar

[19]

S. Saroiu, P. K. Gummadi and S. D. Gribble, A measurement study of peer-to-peer file sharing systems,, Technical Report, (2001), 01.   Google Scholar

[20]

H. Schulzrinne and J. Rosenberg, The session initiation protocol: Internet-centric signaling,, IEEE Communications Magazine, 38 (2000), 134.  doi: 10.1109/35.874980.  Google Scholar

[21]

K. Singh and H. Schulzrinne, SIPpeer: a session initiation protocol (SIP)-based peer-to-peer Internet telephony client adaptor,, , ().   Google Scholar

[22]

K. Singh and H. Schulzrinne, Peer-to-peer Internet telephony using SIP,, Proceedings of ACM NOSSDAV, (2005), 63.   Google Scholar

[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.  doi: 10.1016/j.peva.2005.01.005.  Google Scholar

[24]

, P2PSIP working group,, , ().   Google Scholar

[25]

, Skype,, , ().   Google Scholar

[26]

, Skype statistics,, , ().   Google Scholar

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