Analytical study of multifractal invariant attributes of traffic flows

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.170212

Keywords:

traffic flow, unmanned vehicle, Cantor α-set, multifractality, fragmentation parameter

Abstract

The motor transport complex is formed by a multitude of motor traffic flows and a network of automobile roads. Transition to a new level of the motor functioning transport complex requires the development of new methods of formalizing the collective interaction of all road users. This is connected to an increase in the number of autonomous vehicles in joint traffic. We established that the transport-technological self-organization of motor transport flows is a multifractal structure. Such a structure is reliably enough described by regular hierarchical ‒ sets of Cantor regarding the parameter of the dynamic dimension of an individual vehicle. We proved that the main multifractal attributes of road traffic flows are their fragmentation parameter and fractal dimensionality. These attributes are functionally determined by the speed, traffic density and interval of vehicles movement. Accordingly, there are three modes of vehicles movement. The absence of mutual obstacles between vehicles, low speed and low traffic intensity characterizes free movement. Such a movement determines the boundary of the collective and synchronized flows. Collective movement is characterized by a high density of traffic flow, and speed is limited by the possibilities of the road. If the indicators of the technical and operational condition of the road become decisive, we get a saturated synchronized flow. Analytical studies established a log-exponential functional relationship between the fragmentation parameter of the motor flow and the fractal dimension. We found that the combination of several road traffic flows in the case of multi-lane traffic management determines the dynamics of changes in the basic multifractal characteristics of vehicles variety. At the same time, an increase in the number of road lanes leads to an increase in the fragmentation parameter and a decrease in the fractal dimension of motor traffic flows aggregate. We considered the possibility of creating appropriate navigation algorithms for the variable optimization of the fractal attributes of road traffic. In this case, safe transport and technological modes of the motor transport complex are provided. The same applies to the conditions for increasing the part of autonomous robotic unmanned vehicles in the composition of motor vehicles.

Author Biographies

Oleh Skydan, Zhytomyr National Agroecological University Staryi blvd., 7, Zhytomyr, Ukraine, 10008

Doctor of Economic Sciences, Professor

Department of Innovative Entrepreneurship and Investment Activities

Bogdan Sheludchenko, Scientific-Innovative Institute of Engineering of Agro-Industrial Production and Energy Efficiency Staryi blvd., 7, Zhytomyr, Ukraine, 10008

PhD, Professor

Savelii Kukharets, Zhytomyr National Agroecological University Staryi blvd., 7, Zhytomyr, Ukraine, 10008

Doctor of Technical Sciences, Associate Professor, Head of Department

Department of mechanical engineering and agroecosystems

Oleksandr Medvedskyi, Zhytomyr National Agroecological University Staryi blvd., 7, Zhytomyr, Ukraine, 10008

PhD

Department of Processes, Machines and Equipment in Agroengineering

Yaroslav Yarosh, Zhytomyr National Agroecological University Staryi blvd., 7, Zhytomyr, Ukraine, 10008

PhD, Associate Professor

Department of Processes, Machines and Equipment in Agroengineering

References

  1. Sheludchenko, B. A. (2014). Vstup do konstruiuvannia pryrodno-tekhnohennykh heoekosystem (landshaftno-terytorialnyi aspekt). Kamianets-Podilskyi: Vyd-vo PDATU, 170.
  2. Yang, S., Wu, J., Xu, Y., Yang, T. (2019). Revealing heterogeneous spatiotemporal traffic flow patterns of urban road network via tensor decomposition-based clustering approach. Physica A: Statistical Mechanics and its Applications, 526, 120688. doi: https://doi.org/10.1016/j.physa.2019.03.053
  3. Chen, X., He, Z., Wang, J. (2018). Spatial-temporal traffic speed patterns discovery and incomplete data recovery via SVD-combined tensor decomposition. Transportation Research Part C: Emerging Technologies, 86, 59–77. doi: https://doi.org/10.1016/j.trc.2017.10.023
  4. Kawasaki, Y., Hara, Y., Kuwahara, M. (2019). Traffic state estimation on a two-dimensional network by a state-space model. Transportation Research Part C: Emerging Technologies. doi: https://doi.org/10.1016/j.trc.2019.03.016
  5. Balhanov, V. K. (2013). Osnovy fraktal'noy geometrii i fraktal'nogo ischisleniya. Ulan-Ude, 224.
  6. Babkov, V. F. (1980). Landshaftnoe proektirovanie avtomobil'nyh dorog. Moscow: Transport, 189.
  7. Lukanin, V. N., Trofimenko, Yu. V. (2001). Promyshlenno-transportnaya ekologiya. Moscow: Vysshaya shkola, 273.
  8. Sheludchenko, L. S. (2018). Functional characters of the motor vehicle flow. Vehicle and Electronics. Innovative Technologies, 13, 75–79. doi: https://doi.org/10.30977/VEIT.2018.13.0.75
  9. Mohebifard, R., Hajbabaie, A. (2019). Optimal network-level traffic signal control: A benders decomposition-based solution algorithm. Transportation Research Part B: Methodological, 121, 252–274. doi: https://doi.org/10.1016/j.trb.2019.01.012
  10. Li, L., Li, X. (2019). Parsimonious trajectory design of connected automated traffic. Transportation Research Part B: Methodological, 119, 1–21. doi: https://doi.org/10.1016/j.trb.2018.11.006
  11. Zhang, Y., Ioannou, P. A. (2018). Stability analysis and variable speed limit control of a traffic flow model. Transportation Research Part B: Methodological, 118, 31–65. doi: https://doi.org/10.1016/j.trb.2018.10.005
  12. Batista, S. F. A., Leclercq, L., Geroliminis, N. (2019). Estimation of regional trip length distributions for the calibration of the aggregated network traffic models. Transportation Research Part B: Methodological, 122, 192–217. doi: https://doi.org/10.1016/j.trb.2019.02.009
  13. Mariotte, G., Leclercq, L. (2019). Flow exchanges in multi-reservoir systems with spillbacks. Transportation Research Part B: Methodological, 122, 327–349. doi: https://doi.org/10.1016/j.trb.2019.02.014
  14. Mandelbrot, B. B. (1983). The Fractal Geometry of Nature. W. H. Freeman and Company, 468.

Downloads

Published

2019-06-12

How to Cite

Skydan, O., Sheludchenko, B., Kukharets, S., Medvedskyi, O., & Yarosh, Y. (2019). Analytical study of multifractal invariant attributes of traffic flows. Eastern-European Journal of Enterprise Technologies, 3(3 (99), 22–29. https://doi.org/10.15587/1729-4061.2019.170212

Issue

Section

Control processes