Asymptotic traffic flow in a hyperbolic network

5th International Symposium on Communications Control and Signal Processing, ISCCSP 2012

Volumn , Issue , 2012, Pages

  Baryshnikov, Yuliy ^a   Tucci, Gabriel H ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

Complex Networks; Congestion; Hyperbolic Networks; Spectral Gap; Traffic Load

Indexed keywords

COMPLEX NETWORKS; CONGESTED NODES; CONGESTION; HYPERBOLIC GRAPHS; SPECTRAL GAP; TRAFFIC FLOW; TRAFFIC LOADS; TRAFFIC RATE;

PACKET NETWORKS; SIGNAL PROCESSING;

TRAFFIC CONGESTION;

EID: 84864131585     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISCCSP.2012.6217862     Document Type: Conference Paper

References (16)

1. Y. Baryshnikov and G. Tucci, Asymptotic traffic flow in an Hyperbolic Network I : Definition and Properties of the Core, preprint at http://arxiv.org/abs/1010.3304.
2. Y. Baryshnikov and G. Tucci, Asymptotic traffic flow in an Hyperbolic Network II: Non-uniform Traffic, preprint at http://arxiv.org/abs/1010.3305.
3. L. Barthold and T. Ceccherini-Silberstein, Salem Numbers and Growth Series of Some Hyperbolic Graphs, Geometriae Dedicata Vol. 90, No. 1, pp. 107-114, 2002. (Pubitemid 37141576)
4. S. Blach̀ere, P. Hässinsky and P. Mathieu, Harmonic measures versus quasi-conformal measures for hyperbolic groups, arXiv:0806.3915v1.
5. M. Bonk and B. Kleiner, Rigidity for quasi-Mobius group actions, J. Differential Geom. 61, no. 1, 81-106, 2002.
6. M. Coornaert, Measures de Patterson-Sullivan sur le bord d'un espace hyperbolique au sens de Gromov, Pacific J. Math. 159, no. 2, 241-270, 1993.
7. M. Coornaert, T. Delzant and A. Papadopoulos, Geometrie et theorie des groupes, Springer-Verlag, Berlin, 1993.
8. M. Gromov, Hyperbolic groups, Essays in group theory, Springer, New York, 1987, pp. 75-263.
9. E. Jonckheere, P. Lohsoonthorn and F. Bonahon, Scaled Gromov hyperbolic graphs, Journal of Graph Theory, vol. 57, pp. 157-180, 2008. (Pubitemid 351213233)
10. E. Jonckheere, M. Lou, F. Bonahon and Y. Baryshnikov, Euclidean versus hyperbolic congestion in idealized versus experimental networks, http://arxiv.org/abs/0911.2538.
11. D. Krioukov, F. Papadopoulos, A. Vahdat and M. Boguna, Curvature and temperature of complex networks, Physical Review E, 80:035101(R), 2009.
12. P. Lohsoonthorn, Hyperbolic Geometry of Networks, Ph.D. Thesis, Department of Electrical Engineering, University of Southern California, 2003. Available at http://eudoxus.usc.edu/iw/mattfinalthesis main.pdf.
13. M. Lou, Traffic pattern analysis in negatively curved networks, Ph.D. Thesis, USC, May 2008. Available at http://eudoxus.usc.edu/iw/Mingji-PhD-Thesis. pdf.
14. O. Narayan and I. Saniee, The large scale curvature of networks, Available at http://arxiv.org/0907.1478.
15. D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Etudes Sci. Publ. Math., no. 50, 171-202, 1979.
16. Ya. B. Pessin, Dimension theory in dynamical systems, Chicago Lect. Notes in Math., 1997