Markov Chain methods for analyzing urban networks

Journal of Statistical Physics

Volumn 132, Issue 6, 2008, Pages 1051-1069

  Volchenkov, D ^a   Blanchard, P ^a  

^a BIELEFELD UNIVERSITY   (Germany)

Author keywords

Complex networks; Random walks; Traffic equilibrium

Indexed keywords

EID: 50249175562     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9591-2     Document Type: Article

References (41)

1. Braess, D.: Über ein Paradoxon aus der Verkehrsplannung. Unternehmensforschung 12, 258-268 (1968)
2. Kolata, G.: What if they closed the 42nd Street and nobody noticed? The New York Times, Dec. 25 (1990)
3. Alexanderson, G.L.: Bull. Am. Math. Soc. 43, 567-573 (2006)
4. Hillier, B., Hanson, J.: The Social Logic of Space. Cambridge University Press, Cambridge (1984). ISBN 0-521-36784-0
5. Hillier, B.: Space is the Machine: A Configurational Theory of Architecture. Cambridge University Press, Cambridge (1999). ISBN 0-521-64528-X
6. Rosvall, M., Trusina, A., Minnhagen, P., Sneppen, K.: Phys. Rev. Lett. 94, 028701 (2005)
7. Cardillo, A., Scellato, S., Latora, V., Porta, S.: Phys. Rev. E 73, 066107 (2006)
8. Porta, S., Crucitti, P., Latora, V.: Physica A 369, 853 (2006)
9. Scellato, S., Gardillo, A., Latora, V., Porta, S.: Eur. Phys. J. B 50, 221 (2006)
10. Crucitti, P., Latora, V., Porta, S.: Chaos 16, 015113 (2006)
11. Volchenkov, D., Blanchard, Ph.: Phys. Rev. E 75(2) (2007)
12. Volchenkov, D., Blanchard, Ph.: Physica A 387(10), 2353-2364 (2008). doi: 10.1016/j.physa.2007.11.049
13. Gross, D., Harris, C.M.: Fundamentals of Queueing Theory. Wiley, New York (1998)
14. Backus, B.T., Oruç, I.: J. Vis. 5(11), 1055-1069 (2005)
15. Biggs, N.: Permutation Groups and Combinatorial Structures. Cambridge University Press, Cambridge (1979)
16. Blanchard, Ph., Volchenkov, D.: Intelligibility and first passage times in complex urban networks. Proc. R. Soc. A 464, 2153-2167 (2008). doi: 10.1098/rspa.2007.0329
17. Lagrange, J.-L.: Uvres, vol. 1, pp. 72-79. Gauthier-Villars, Paris (1867) (in French)
18. Lovász, L.: Combinatorics, Paul Erdös is Eighty. Bolyai Society Mathematical Studies, vol. 2, pp. 1-46. Bolyai Mathematical Society, Keszthely (1993)
19. Aldous, D.J., Fill, J.A.: Reversible Markov chains and random walks on graphs (in preparation). See http://www.stat.berkeley.edu/waldous/RWG/book.html
20. Chung, F.: Lecture Notes on Spectral Graph Theory. AMS, Providence (1997)
21. Farkas, I.J., Derényi, I., Barabási, A.-L., Vicsek, T.: Phys. Rev. E 64, 026704 (2001)
22. Farkas, I., Derényi, I., Jeong, H., Neda, Z., Oltvai, Z.N., Ravasz, E., Schubert, A., Barabási, A.-L., Vicsek, T.: Physic A 314, 25 (2002)
23. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)
24. Sinai, Ya.G., Soshnikov, A.B.: Funct. Anal. Appl. 32(2), 114-131 (1998)
25. Arnold, L.: Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 19, 191-198 (1971)
26. Alon, N., Krivelevich, M., Vu, V.H.: Isr. J. Math. 131, 259-267 (2002)
27. Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F., Samukhin, A.N.: Phys. Rev. E 68, 046109 (2003)
28. Eriksen, K.A., Simonsen, I., Maslov, S., Sneppen, K.: Phys. Rev. Lett. 90(14), 148701 (2003)
29. Chung, F., Lu, L., Vu, V.: Proc. Natl. Acad. Sci. USA 100(11), 6313-6318 (2003). Published online doi:10.1073/pnas.0937490100
30. Bollobás, B., Riordan, O.: Mathematical results on scale-free random graphs. In: Handbook of Graphs and Networks. Wiley, New York (2002)
31. Bianconi, G., Gulbahce, N., Motter, A.E.: Local structure of directed networks, 27 July 2007. E-print arXiv:0707.4084 [cond-mat.dis-nn]
32. Chung, F.: Ann. Comb. 9, 1-19 (2005)
33. Lovász, L., Winkler, P.: Mixing of random walks and other diffusions on a graph. In: Surveys in Combinatorics, Stirling. London Math. Soc. Lecture Note Ser., vol. 218, 119-154. Cambridge Univ. Press, Cambridge (1995)
34. Bjöner, A., Lovász, L., Shor, P.: Eur. J. Comb. 12, 283-291 (1991)
35. Bjöner, A., Lovász, L.: J. Algebr. Comb. 1, 305-328 (1992)
36. Butler, S.: Electron. J. Linear Algebra 16, 90 (2007)
37. Aubry, N., Guyonnet, R., Lima, R.: J. Stat. Phys. 64, 683-739 (1991)
38. Aubry, N.: Theor. Comput. Fluid Dyn. 2, 339-352 (1991)
39. Karhunen, K.: Ann. Acad. Sci. Fenn. A 1 (1944)
40. Loève, M.: Probability Theory. van Nostrand, New York (1955)
41. Aubry, N., Lima, L.: Spatio-temporal symmetries. Preprint CPT-93/P. 2923, Centre de Physique Theorique, Luminy, Marseille, France (1993)