Algorithm Model for the Operation of Traffic Light Cycles at the Transport Network Intersections

Abstract

The subject of the research is the mathematical model development for constructing an algorithm of the traffic light operation, providing adaptive control of vehicles at intersections of the urban transport network. In the process of functioning of urban transport networks, such phenomena as traffic jams of vehicles arise, which lead to significant economic losses, environmental degradation, frustration of road users and other types of negative impacts. Traffic jams often occur at nodes of the urban transport network that are intersections – places where roads of the urban network of the same level intersect, join or branch off. One of the reasons of traffic jams is the ineffective management of traffic flows at intersections, which is ensured by such an element of the intersection as a traffic light. Within the existing transport network, traffic lights implementing adaptive control with the help of corresponding local controllers and more complex system controllers created on their basis, taking into account the situation in the external environment, which is represented by several interconnected intersections, are currently one of the most important areas for solving congestion problems. The traffic light’s flow control function is implemented using a microprocessor controller, which, according to a given algorithm, switches the colours of the traffic light corresponding to the phases of permission and prohibition of vehicle movement in the directions of the intersection roads.

The article gives a mathematical model for constructing an algorithm for the operation of a microprocessor traffic light controller, which ensures prompt and adequate display of situations at intersections. The main features of the model include the prompt response to changing situations at the intersection by changing the duration of the permissive phase of movement in each cycle of the traffic light operation in proportion to the length of the queue of vehicles in the corresponding direction of movement; adequate display of the external environment by several expressions of the Poisson law, differing in different parameter values, each of which corresponds to a certain daily interval of traffic light operation; the dynamics of changes in the traffic situation caused by a decrease in the number of vehicles in a queue due to vehicles passing through an intersection during the green phase of the traffic light, which is determined on the basis of expressions that define the movement of bodies during uniformly accelerated and uniform motion, as well as on the basis of the differential equation for the dynamics of the movement of vehicles in one row, taking into account the delay caused by the reaction of drivers.