Deterministic-stochastic model of heterogeneous auto transport flow
Abstract
The structure of the traffic flow can be characterized by the types of vehicles, the degree of their load with objects of transportation, as well as traffic modes.
Mathematical modeling helps to describe the state of the traffic flow and study its characteristics. With its help, it is possible to develop a number of models for the transport system that will help solve practical problems. Depending on the tasks to be solved, models can be classified by approaches, description and level of problem solving. There are several large groups classified by approaches: macroscopic, microscopic, models of cellular automata and probabilistic models. In the classification according to the level of problem solving, predictive, simulation and optimization models are distinguished.
When modeling traffic flows, a large number of factors with different change intervals should be taken into account: road capacity, road surface quality, drivers' reactions, vehicle operation algorithms. Analyzing these factors, it is possible to conclude that transport flows have such properties as: stochasticity, non-stationarity, spatial and temporal, as well as informational.
Stochasticity occurs most often due to the human factor. The behavior of a vehicle on the road can only be predicted with a certain probability by dividing the vehicles into groups. Such behavior cannot be described only by the laws of solid mechanics.
Non-stationarity occurs due to changes in weather conditions, traffic conditions, time of day, season.
In modern science, transport models were considered from the point of view of two approaches: probabilistic, which uses the methods of mass service theory, and hydrodynamic, which reduces the transport flow to the solution of hydrodynamic equations.
Among the approaches, deterministic-stochastic can also be distinguished, which is used further to build the model. This approach takes into account two components: deterministic and stochastic. In the first, all the factors affecting decision-making are taken into account and known in advance, in the second there is an element of uncertainty, which depends on the probability of maneuvering cars inside the stream.
The stochastic approach makes it possible to differentiate the behavior of road users. Therefore, with its help, you can fine-tune the mathematical model.
The circumstances described above indicate the relevance of developing a mathematical model of heterogeneous traffic flow, which is based on a deterministic-stochastic approach.
Key words: traffic flow, deterministic-stochastic model, probability, traffic model, traffic lane, flow intensity, flow density, flow speed, driver reaction time.
