Model And Algorithm Of User Equilibrium Traffic Assignment Under Left-Turn Prohibition

With the increase of urban cars, traffic jam becomes more and more serious, not only giving rise to the environmental pollution, but also resulting in more and more traffic accidents. In addition, the left-turn of vehicles at intersections has the larger impact to traffic flow, and it becomes the main factor leading to urban traffic congestions and accidents. As such, many cities prohibit direct left-turns to keep traffic moving efficient on major roads. However, how do drivers choose their travel paths under left-turn prohibitions? Will the additional traveling distance of drivers’ other alternatives aggravate the total travel time of traffic network or increase the total traffic emissions? Where should authorities implement left-turn prohibitions, if they wish to minimize the total travel time of the network or make the traffic network system optimization from the view of environmental protection? For these questions, this paper proposes a bi-level programming model utilizing the User Equilibrium (UE) theory, gives out the relevant algorithm, and improves the algorithm.There are three main parts discussed in this paper:Part I, we introduce the characteristics and applications of left-turn prohibition, analyze the advantages and disadvantages brought by left-turn prohibition to the traffic network, as well as illustrate the manners of drivers’other alternatives under left-turn prohibition.Part II, we propose a bi-level mathematical model for left-turn prohibition planning utilizing the User Equilibrium theory. We use the Frank-Wolfe algorithm to assign traffic demand for vehicles in the lower-level model, and calculate the weighted combination of total travel time and total traffic emissions, then determine where to implement left-turn prohibition in the upper-level model, using a Genetic Algorithm, such that the traffic network system is optimized. In addition, we carry on an improved algorithm for upper-level model, which can effectively enhance the speed and accuracy of the calculation.Part Ⅲ, instance application, considering two circumstances including conventional network and irregular network. By numerical example, we show that both the total travel time and the total traffic emissions can be reduced by implementing the left-turn prohibition at some carefully selected intersections. Therefore, from the view of environmental protection, the research in this paper is expected to be useful in transportation planning and management.