INVESTIGATION OF SCALE-INVARIANT PROPERTY  OF ORGANIZATION SYSTEM OF TRAIN TRAFFIC  VOLUME BASED ON THE PERCOLATION THEORY

A. V. Prokhorchenko

doi:10.15802/stp2014/30471

Authors

A. V. Prokhorchenko Ukrainian State Academy of Railway Transport, Ukraine https://orcid.org/0000-0003-3123-5024

DOI:

https://doi.org/10.15802/stp2014/30471

Keywords:

scale-invariant networks, trains′ formation plan, percolation, survivability, graph, railway network

Abstract

Purpose. The work is devoted to the study the property of scaling invariance of the organization system of train traffic volume on Ukrainian railways. Methodology. To prove the real network origin of Trains Formation Plan (TFP) destination to the type of socalled scale-invariant networks it is proposed to generate scale-free networks with different dimensions, Barabási–Albert type with parameters that real networks of TFP destination has and to investigate their structure on survivability using the procedure of percolation nodes. Percolation process is proposed to be considered as a modified version of the spatial movement of cars on the network by increasing the number of railway stations, which have lost the ability to perform the basic function to pass cars on TFP destination in terms of adverse effects (an accident, overload). Findings. Comparative analysis of percolation at random and targeted destructive impact on network nodes has shown matching with the results of real network percolation of TFP destination, which proves the existence of self-similarity. Comparable figures in percolation were: percentage of remote stations in the network, in which the network fragmentation occurs, the average inverse path between network nodes, the diameter of the graph structure, the size meaning of the second largest cluster in the network from the steps of destruction. Originality. For the first time the hypothesis of the existence of scaling invariance properties of the graph TFP destinations on the railways of Ukraine, which can be attributed to a class of the graph scale-free networks was confirmed. Existing knowledge in the field theory of scale-free networks can be used to describe the survivability of system transportation on the railways of Ukraine. Practical value. Based on the identified properties of system directions of train traffic volumes, it is possible to create a mathematical model in the future that will predict the behavior of the transportation system with network structure. Properties analysis of system survivability of train traffic volumes will optimize the use of capital investments to increase network capacity by identifying the most critical lines and stations that systematically affect the efficiency of the network as a whole.

Author Biography

A. V. Prokhorchenko, Ukrainian State Academy of Railway Transport

Dep. «Operational Work Management»

References

Bobrovskiy V.I., Skovron I.Ya. Sovershenstvovaniye tekhnologii formirovaniya mnogogruppnykh sostavov [Improving the technology of multigroup compositions formation]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2007, issue 19, pp. 88-93.

DSTU 2860-94. Nadiinist tekhniky. Terminy ta vyznachennia [State Standard of Ukraine 2860-94. Reliability of technique. Terms and Definitions]. Kyiv, Derzhstandart Ukrainy Publ., 1994. 33 p.

Martseniuk L.V., Vyshniakova A.V. Vdoskonalennia protsesu vantazhnykh perevezen ta mekhanizmu upravlinnia nymy [Improving of freight transportation process and mechanism of their management]. Nauka ta prohres transportu. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu − Science and Transport Progress. Bulletin of Dnipropetrovsk National University of Railway Transport, 2014, no. 2 (50), pp. 41-48.

Prokhorchenko A.V. Analiz zhyvuchosti systemy orhanizatsii poizdopotokiv na osnovi teorii perkoliatsii [Analysis of survivability of the organisation system of train traffic volumes on the percolation theory]. Vostochno-yevropeyskiy zhurnal peredovykh tekhnologiy – Eastern-European Journal of Innovativee Technologies, 2013, vol. 6, no. 3 (66), pp. 7-10.

Holovach Yu., Oliemskoi O., fon Ferber K., Holovach T., Mryhlod O., Olemskoi I., Palchykov V. Skladnі merezhі [Complex networks]. Zhurnal fіzychnykh doslіdzhen – Journal of Physical Studies, 2006, vol. 10, no. 4, pp. 247-289.

Tarasevich Yu.Yu. Perkolyatsiya: teoriya, prilozheniya, algoritmy [Percolation: theory, applications, algorithms].Moscow, Editorial URSS Publ., 2002. 112 p.

Albert R., Jeong H., Barabasi A. Attack and error tolerance of complex networks. Nature, 2000, vol. 406. pp. 378–382.

Albert R., Barabási A.-L. Statistical mechanics of complex networks. Reviews of Modern Physics, 2002, vol. 74, pp. 47-97.

Barabási A.-L., Albert R. Emergence of scaling in random networks. Science, 1999, vol. 286, pp. 509-512. doi: 10.1126/science.286.5439.509.

Batagelj V., Mrvar A. Pajek: Package for Large Networks, Version 1.10. Ljubljana,University ofLjubljana Publ., 2005. 10 p.

Broadbent S.R., Hammersley J.M. Percolation processes: I. Crystals and Mazes. Mathematical Proc. of theCambridgePhilosofical Society, 1957, vol. 53, pp. 629-641.

But’ko T., Prokhorchenko A. Investigation into Train Flow System on Ukraine’s Railways with Methods of Complex Network Analysis. American Journal of Industrial Engineering, 2013, vol. 1 (3), pp. 41-45.

Clauset A., Clauset A., Shalizi C.R., Newman M.E.J. Powerlaw distributions in empirical data. SIAM Review, 2009, vol. 51 (4), pp. 661-703. doi: 10.1137/070710111.

Ballesteros H.G., Fernández L.A., Martin-Mayor V., Parisi G., Ruiz-Lorenzo J.J. Measures of critical exponents in the four dimensional site percolation. Physics Letters, 1997, vol. 400 (3) B, pp. 346-351. doi: 10. 1016/s0370-2693(97)00337-7.

Newman M.E.J., Watts D.J. Scaling and percolation in the small-world network model. Phys. Rev. E., 1999, vol. E 60 (6), pp. 7332-7342. doi: 10.1103/physreve.60.7332.

Wasserman, S., Faust K. Social Network Analysis: Methods and Applications. Cambridge, Cambridge University Press Publ., 1994. 827 p.