Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-12T15:25:57.539Z Has data issue: false hasContentIssue false
  • English
  • Français

Interacting branching processes and linear file-sharing networks

Part of: Operations research and management science Markov processes

Published online by Cambridge University Press:  01 July 2016

Lasse Leskelä ,
Philippe Robert  and
Florian Simatos
Lasse Leskelä*
Affiliation:
Helsinki University of Technology
Philippe Robert*
Affiliation:
INRIA Paris-Rocquencourt
Florian Simatos*
Affiliation:
INRIA Paris-Rocquencourt
*
∗ Current address: Aalto University, Department of Mathematics and Systems Analysis, PO Box 11100, 00076 Aalto, Finland. Email address: lasse.leskela@iki.fi
∗∗ Postal address: INRIA Paris-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay, France.
∗∗ Postal address: INRIA Paris-Rocquencourt, Domaine de Voluceau, BP 105, 78153 Le Chesnay, France.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

File-sharing networks are distributed systems used to disseminate files among nodes of a communication network. The general simple principle of these systems is that once a node has retrieved a file, it may become a server for this file. In this paper, the capacity of these networks is analyzed with a stochastic model when there is a constant flow of incoming requests for a given file. It is shown that the problem can be solved by analyzing the asymptotic behavior of a class of interacting branching processes. Several results of independent interest concerning these branching processes are derived and then used to study the file-sharing systems.

Keywords

Interacting branching processpeer-to-peer algorithm

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes
Secondary: 90B18: Communication networks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 3 , September 2010 , pp. 834 - 854
Copyright
Copyright © Applied Probability Trust 2010 

References

Aldous, D. and Pitman, J. (1998). Tree-valued Markov chains derived from Galton–Watson processes. Ann. Inst. H. Poincaré Prob. Statist. 34, 637–686.CrossRefGoogle Scholar
Alsmeyer, G. (1993). On the Galton–Watson predator-prey process. Ann. Appl. Prob. 3, 198–211.CrossRefGoogle Scholar
Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, New York.CrossRefGoogle Scholar
Bramson, M. (2008). Stability of Queueing Networks (Lecture Notes Math. 1950). Springer, Berlin.Google Scholar
Chen, H. and Yao, D. D. (2001). Fundamentals of Queueing Networks. Springer, New York.CrossRefGoogle Scholar
Kingman, J. F. C. (1975). The first birth problem for an age-dependent branching process. Ann. Prob. 3, 790–801.CrossRefGoogle Scholar
Lamperti, J. (1967). Continuous state branching processes. Bull. Amer. Math. Soc. 73, 382–386.CrossRefGoogle Scholar
Leskelä, L. (2010). Stochastic relations of random variables and processes. J. Theoret. Prob. 23, 523–546.CrossRefGoogle Scholar
Massoulié, L. and Vojnović, M. (2005). Coupon replication systems. In Proc. ACM SIGMETRICS 2005, ACM Press, New York, pp. 2–13.Google Scholar
Nerman, O. (1981). On the convergence of supercritical general (C-M-J) branching processes. Z. Wahrscheinlichkeitsth. 57, 365–395.CrossRefGoogle Scholar
Neveu, J. (1986). Erasing a branching tree. In Analytic and Geometric Stochastics (Papers in honour of G. E. H. Reuter; Adv. Appl. Prob. Spec. Suppl. 19), ed. Kendall, D. G., Applied Probability Trust, Sheffield, pp. 101–108.Google Scholar
Núñez-Queija, R. and Prabhu, B. J. (2008). Scaling laws for file dissemination in P2P networks with random contacts. In Proc. 16th Internat. Workshop on Quality of Service, IEEE, pp. 75–79.Google Scholar
Qiu, D. and Srikant, R. (2004). Modeling and performance analysis of BitTorrent-like peer-to-peer networks. In Proc. 2004 Conf. on Applications, Technologies, Architectures, and Protocols for Computer Communications, ACM Press, New York, pp. 367–378.Google Scholar
Robert, P. (2003). Stochastic Networks and Queues (Appl. Math. 52). Springer, Berlin.CrossRefGoogle Scholar
Rogers, L. C. G. and Williams, D. (1987). Diffusions, Markov Processes, and Martingales, Vol. 2. John Wiley, New York.Google Scholar
Seneta, E. (1970). On the supercritical branching process with immigration. Math. Biosci. 7, 9–14.CrossRefGoogle Scholar
Simatos, F., Robert, P. and Guillemin, F. (2008). A queueing system for modeling a file sharing principle. In Proc. ACM SIGMETRICS 2008, ACM Press, New York, pp. 181–192.Google Scholar
Susitaival, R., Aalto, S. and Virtamo, J. (2006). Analyzing the dynamics and resource usage of P2P file sharing by a spatio-temporal model. In Comptutational Science – ICCS 2006 (Lecture Notes Comput. Sci. 3994), Springer, Berlin, pp. 420–427.CrossRefGoogle Scholar
Trang, D. D., Pereczes, R. and Molnár, S. (2007). Modeling the population of file-sharing peer-to-peer networks with branching processes. In IEEE Symp. Comput. Commun. (Aveiro, Portugal, July 2007), pp. 809–815.Google Scholar
Williams, D. (1991). Probability with Martingales. Cambridge University Press.CrossRefGoogle Scholar
Yang, X. and de Veciana, G. (2004). Service capacity of peer to peer networks. In Proc. IEEE INFOCOM, ACM Press, New York, pp. 2242–2252.Google Scholar