Forecasting the congestion of the streets of large cities, taking into account fluctuations in the density and speed of traffic flows

The work has developed a methodical approach for forecasting the congestion of the streets of large cities, taking into account the fluctuations in the density of traffic flows and the speed of movement of cars in the traffic flow, which are associated with "peak hours". The methodological approach, unlike the previously known ones, complements the well-known robustness criterion developed by the authors in previous publications, which allows to increase the accuracy of forecasting the occurrence of traffic jams. Time-varying functions of traffic flow density and vehicle speed in the traffic flow are proposed. In addition to real time, functions contain variable parameters in the form of amplitude of oscillations and period of oscillations. This makes it possible to adapt the forecasting model to the real road network, taking into account the period of network congestion and road infrastructure. The dependences of the change in the range of robustness of the traffic flow when the density and speed of movement of vehicles in the flow change. It has been proven that in the presence of fluctuations of the listed parameters, the appearance of traffic jams occurs at average values of density and speed. A significant influence of the amplitude of fluctuations in the density and speed of movement of vehicles in the stream on the appearance of traffic jams has been proven. It is shown that the magnitude of the amplitude of oscillations during "peak times" significantly reduces the stability range of the traffic flow. The influence of the "peak hour" period on the loss of stability of the traffic flow is given. It has been proven that the period of oscillations is an insignificant factor in forecasting traffic jams. However, accounting for such a factor will allow to adapt the mathematical model to the real conditions of traffic flow behavior and thereby increase the accuracy of forecasting. It is shown that accounting for the fluctuating component of the traffic flow expands the possibilities of applying the robustness criterion presented by the authors in previous publications and makes it possible to provide a more accurate forecast for various sections of the road network of large cities.