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.

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We examine the modeling 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. Keywords Reversible lane · road traffic control · mathematical modeling AcknowledgementThe project presented in this article is supported by OTKA CNK 78168.This work is connected to the scientific program of the " Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project.

Road traffic flows on a straight road segment such as bridges are modelled in this article. The mathematical model of traffic flows has been constructed by using the method of lumped parameters. Changeable lane direction and road pricing has been theoretically investigated in order to understand the shifting in supply and/or demand curves of traffic participants in equilibrium. The article presents assumptions for constructing the mathematical model. Demand can be influenced by road pricing, in its turn, supply can be influenced by extension of infrastructure with reversible lanes.

Optimization of traffic on a large public road network is a complex task. Reversible direction lane theory is an interesting and special method within this subject. This can completely support the fluctuation or alteration of main congested directions existing in the traffic dynamics (time of day, seasonal, etc.) on the 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 structure of the system 'in an optimal direction' , but many practical and safety questions arise. The authors have examined the modelling of a Reversible Lane System (RLS) created based on a simple part of a road network, which is segmented into elements. Functions of each network element and contacts between them cease operating in the course of such change while new contacts and new function elements are activated instead. The article presents the mathematical modelling of the problem. It points out the fundamental questions of the structure change and exemplifies the above using a simple example. The authors studied a general mathematical model describing the RLS. They examined the availability of the optimal control in a sample network depending on the traffic density, using a new principle, which responds to the dynamic change of the structure of the network graph. It can be shown, that the results from the model are in harmony with the real traffic values based on measurements made in road traffic systems working with RLS. Reference to this paper should be made as follows: Bede, Z.; Péter, T. 2014. Optimal control with the dynamic change of the structure of the road network, Transport 29(1): 36-42. http://dx.