Analytical study of multifractal invariant attributes of traffic flows

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.