Integrated optimization of lane allocation and adaptive signal control at isolated intersection under stochastic demand

Traffic arrival rate at intersections is usually fluctuating and random. This paper proposes an integrated optimization method for lane allocation and signal control under stochastic demand using the concept of level-of-service (LOS) reliability. First, we develop a two-stage stochastic programming model. In the first stage, a base lane allocation plan that takes account of the arrival uncertainty is derived. The objective is to minimize the expected average delay of the intersection. At the second stage, upon realizations of the random arrivals, the signal timing plan is adjusted in respond to the varying traffic conditions and address the occasional overflows, which may occur with the base lane allocation plan. In view of the intertwined two-stage decisions, we introduce the LOS reliability to decouple the model into two independent subproblems for solution efficiency. A decoupled model is then reconstructed with a LOS reliability constraint, which is associated with a fixed traffic arrival pattern. Then, a gradient descent algorithm is developed to solve the optimal LOS reliability level. Numerical experiments on both a test intersection and a real intersection are conducted and two benchmark methods are introduced for comparison. Experimental results demonstrate the effectiveness of the proposed LOS reliability-based optimization method in terms of reducing the expected average delay. With the benefits from a robust base lane allocation plan, the optimal signal timing plans can better adapt to random traffic demands.