MATHEMATICAL MODEL OF ADAPTIVE CONTROL OF THE FUNCTIONING OF A TRAFFIC LIGHT AT THE CROSSROADS OF A URBAN TRANSPORTATION NETWORK

Abstract

The subject of the research is the process of modeling the functioning of a traffic light, providing adaptive control of vehicles at the intersections
of the city transport network. In the process of functioning of urban transport networks, such phenomena as traffic jams occur, which lead to
significant economic losses, environmental degradation, frustration of road users and other types of negative impacts. Traffic jams often occur at the
nodes of the urban transport network, which are intersections - the places of intersection, abutment or branching of roads of the urban network of the
same level. One of the causes of congestion is the ineffective management of traffic flows at intersections, which is provided by such an element of the
intersection as a traffic light. Within the framework of the existing transport network, traffic lights that implement adaptive control with the help of
appropriate local controllers, and more complex system controllers created on their basis, ensuring that the situation in the external environment is
taken into account, which is represented by several interconnected intersections, is currently one of the most important directions for solving the
problem of traffic jams. The traffic light flow control function is implemented using a microprocessor controller, which, according to a given algorithm, switches the traffic light colors corresponding to the phases of allowing and prohibiting the movement of the vehicle in the directions of the
intersection roads.
The article proposes a mathematical model for building an algorithm for the functioning of a microprocessor traffic light controller, which
provides a prompt and adequate display of situations at intersections. The main features of the model include responsiveness to changes in situations at
an intersection by changing the duration of the permissive phase of movement in each cycle of traffic light operation in proportion to the length of the
queue of vehicles in the corresponding direction of travel; adequate display of the external environment by several expressions of Poisson’s law,
differing in different values of the parameter, each of which corresponds to a certain daily interval of traffic light functioning; the dynamics of changes
in the traffic situation due to a decrease in the number of vehicles in the queue due to the passage of the intersection by vehicles during the green phase
of the traffic light is determined on the basis of expressions that determine the movement of bodies with uniformly accelerated and uniform movement,
as well as on the basis of the differential equation of the dynamics of movement of vehicles in one row taking into account the delay caused by the
reaction of drivers.