Abstract
Optimization of traffic on a large public road network is an undertaking and complex task. Reversible Direction Lane theory is an interesting and special method within this subject. This can completely support the fluctuation or alteration in existing congestional direction of traffic dynamics (time of day, seasonal, etc.) on existing road surfaces. In such case certain subsystems of the main network cease to exist, and subsystems working with new connections take their place. This type of routing therefore changes the system’s structure „in an optimal direction”, but many practical and safety questions arise. A number of studies prove that in areas this method is employed, travel time decreased by 30-40%, waiting time by 40-50%, number of stops by 30-40% compared to previous data. Its benefits were also shown in fuel consumption reduced by 15-25%, harmful substance emission HC by 15-25%, CO by 3-5%, and NO by 8-10%. We may not leave the application of this opportunity out of consideration in a case when a country's road infrastructure demands considerable developments otherwise. We examine the modelling of reversible lane system configured on a road part network. The functions of the each network's elements and contacts between its each element cease in the course of a change and new contacts and new function elements are activated instead of them. This opens the door to a new principled optimal control, which happens to the dynamic change of the structure of the network graph. In the model, as in reality, the geometry elements do not disappear naturally, but create a variable network as a result of their new function and their connection system. The article presents the mathematical modeling of the problem. Points out the fundamental questions of the structure change and exemplifies the above on a simple example. We examined a general mathematical model describing the Reversible Lane System. Our descriptive mathematical network model is a positive non-linear dynamic system, and also important that it is a macroscopic model. The function of every element and the contacts between the elements cease in case of direction change in any part of the network, then new contacts and new functional elements are activated. We examined the availability of the optimal control in a sample network depending on the traffic density, using a new principle, which responses to the dynamic change of the structure of the network graph. It can be shown, that the results from our model are in harmony with the real traffic values based on measurements made in road traffic systems working with Reversible Lane System, included in our literature references.
Keywords: Reversible lane, road traffic, traffic control, analysis of risk factors