Optimal control with the dynamic change of the structure of the road network

Abstract

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.

Keywords:

• reversible lane system
• road traffic
• traffic control
• optimal control
• traffic lane
• junction