Abstract
A new approach to the construction of transport entropy models of distribution based on the formalism of nonextensive statistics is proposed. As an example, a simple entropy model is built for single-purpose travels and for a homogenous group of cars. This approach allows simulation of more complicated non-Gibbs distributions. The fundamental principle of the research is the Tsallis nonextensive entropy and degree distributions dependent on the actual number q which is the measure of nonadditive complex socioeconomic systems.
Similar content being viewed by others
References
A. J. Wilson, “Entropy maximizing models in the theory of trip distributions, mode split and route split,” J. Transp. Econ. Policy 3, 108–126 (1969).
A. J. Wilson, “A statistical theory of spatial distribution models,” Transp. Res. 1, 253–269 (1967).
A. J. Wilson, Entropy Methods for Simulation of Complex Systems (Nauka, Moscow, 1978) [in Russian].
A. V. Gsnikov et al., Introduction to Mathematical Simulation of Transport Flows. Handbook, Ed. by A. V. Gasnikov et al. (MTsNMO, Moscow, 2012).
S. C. Fang, J. R. Rajasekera, H.-S.J. Tsao, Entropy Optimization and Mathematical Programming (Kluwer Academic Publisher, 1997).
A. I. Olemskoi, Synergetics of Complex Systems: Phenomenology and Statistical Theory (KRASAND, Moscow, 2009) [in Russian].
W. J. Reed, “On Pareto’s law and the determinants of Pareto exponents,” J. Income Distribution 13, 7–17 (2004).
C. Tsallis, “Possible generalization of Boltzmann-Gibbs statistics,” J. Stat. Phys. 52, 479–487 (1988).
E. M. F. Curado and C. Tsallis, “Generalized statistical mechanics: connection with thermodynamics,” J. Phys., A 24, L69–72 (1991).
Nonextensive statistical mechanics and thermodynamics: Bibliography / http://tsallis.cat.cbpf.br/biblio.htm.
V. Schwammle and C. Tsallis, http://xxx.lanl.gov/arXiv:cond-mat/0703792/
C. Tsallis, R. S. Mendes, and A. R. Plastino, “The role of constraints within generalized Nonextensive statistics,” Physica A 261, 534–554 (1998).
H. Haken, Information and Self-Organization. Macroscopic Approach to Complex Systems (Mir, Moscow, 1991) [in Russian].
G. V. Sheleikhovskii, The Composition of the Urban Plan As a Problem of Transport (GIPROGOR, Moscow, 1946) [in Russian].
L. D. Bregman, “The proof of Shaleikhovskii’s method convergence for the problem of transport constraints,” J. Exp. Theor. Phys., No. 1, 147–156 (1967).
Y. Nesterov and A. Palma de, “Static equilibrium in congested transportation networks,” Networks and Spatial Economics 3, 371–395 (2003).
M. A. Leontovich, Introduction in Thermodynamics. Statistical Physics (Nauka, Moscow, 1983) [in Russian].
S. Martinez, F. Nicolas, F. Pennini, and A. Plastino, “Tsallis’ entropy maximization procedure revisited,” Physica A, 286, 489–502 (2000).
Dynamical foundations of nonextensive statistical mechanics. Preprint [cond-mat/0105374] (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.V. Kolesnichenko, 2014, published in Matematicheskoe Modelirovanie, 2014, Vol. 26, No. 5, pp. 48–64.
Rights and permissions
About this article
Cite this article
Kolesnichenko, A.V. On construction of the entropy transport model based on the formalism of nonextensive statistics. Math Models Comput Simul 6, 587–597 (2014). https://doi.org/10.1134/S2070048214060052
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S2070048214060052