Scientists at St. Petersburg State University, proposed a solution to traffic congestion using mathematical algorithms. Alexander Krylatov and Viktor Zakharov’s research shows in order to improve the transportation in a big city, a balanced change in infrastructure and a unified navigation system can help. A monograph of the mathematicians was published by Springer.

With passenger cars getting more accessible around the world causes a traffic problem for big cities. Scientists have been searching a solution for a long time. Since the late 1950s, the theory of traffic flows has turned into an independent section of applied mathematics. And in the recent decades, the number of works have multiplied.

Alexander Krylatov, Professor of the Department of Mathematical Modeling of Energy Systems at St. Petersburg State University said, “In Russia, the task of organizing traffic historically rests on the shoulders of transport engineers. At the same time, they are more specialized in solutions related to structural changes of individual sections of the network, and do not have competencies in the field of systemic increase in its throughput. Thus, in conditions of ever-increasing traffic flows, even if the engineers manage to achieve local improvements, after a while the traffic flow increases back to old levels and the same congestion occurs in other places.”

The monograph, written by two scientists together, Krylatov who is a professor at the Department of Mathematical Modeling of Energy Systems at St. Petersburg State University, and Viktor Zakharov, Doctor of Physics and Mathematics, presents new mathematical approaches to traffic optimization, as well as possible ways to implement them.

British mathmetician’s theories guided them

The principles that scientists suggest are guided by the formulations of an English mathematician and transport analyst John Glen Wardrop. In 1952, Wardrop offered two principles. The first of them – the principle of equilibrium – is a mathematical construct that allows you to simulate systems, in the case of traffic, assuming that each driver pursues exclusively personal goals. That is why the created models are based on the fact that any changes in traffic flows should be based on the selfish behavior of the drivers.

The second principle – the Wardrop system optimum – states that there is a possibility of managing all vehicles. However, the authors of the monograph precisely emphasized in the first principle that they believe the behavior of drivers can be influenced indirectly – through changes in road infrastructure. Mathematical models allow us to predict how this will change traffic on each local section of the network.

Navigation systems have to sync

The authors note that the navigation systems that we use today have a great influence on the management of traffic flows. In their opinion, the most effective situation would be if all drivers use the same system and receive information on suitable routes from a single center. Otherwise, if one of the major navigators suddenly announces that it will redirect its users so that the traffic situation in the city improves and the other navigators do not support it, the changes will still remain at the local level – the system will rebuild and the problem will not be solved.

Traffic optimization is also possible due to the expansion or narrowing of the roadway, which is especially important in cities with an already existing network. In such cases, it is often impossible to extend the road from intersection to intersection, and the construction of new intersections is not always advisable.

Motorists, electric cars and maybe new roads

Krylatov explained: “Using a mathematical approach, we proved that the best way to improve the topology of the road network is to maximize the possible expansion of the roadbed of the shortest routes between the identified points of departure and arrival of drivers. At the same time, it is necessary to expand the entire route, and not just one or several of streets, otherwise a ‘bottleneck’ may arise. After that, you can proceed to the next most important route for motorists. This is guaranteed to lead to a decrease in the average time of movement in the network as a whole”.

In cases where it is not possible to build roads, it is advisable to use other methods: for example, prohibiting parking through the route. In addition, science can help create dedicated roads for electric vehicles if the city administration wants to motivate drivers to switch to green cars in this way. Especially for them, there can be separate routes planned.

Digital twins can help us foresee the effect of the changes

“Every year, a considerable budget is allocated for improving roads. The mathematical theory of the distribution of traffic flows offers a set of solutions for the effective management of this money,” the scientist said. “In this case, the mathematical approach in this case is superior to the engineering and economic one, as it allows you to analyze the entire transport network, given the complex laws of the mutual influence of its individual elements on each other. We have done a great job in the field of modeling traffic flows and networks. Now we want to move on to the stage of putting our ideas into practice”.

One of the ways to use mathematical models can be the development on their basis of digital twins of transport systems. These simulations, implemented in the form of computer programs, will become an extremely useful intellectual tool in the hands of transport engineers.

“By building digital twins of the transport system and using them to optimize flows, a balance can be achieved between the demand for using the system and the infrastructure capabilities. In the context of the digitalization of the economy, this is unlikely to be dispensed with, ” Viktor Zakharov added.