Distributionally robust lane reservation under uncertain road travel times

Abstract

In this paper, we investigate a new stochastic lane reservation problem under uncertain road travel times. The problem needs to determine an optimal location of reserved lanes in a transportation network and design reserved lanes-based routes for special time-crucial transport tasks under the condition that the travel time is uncertain, but partial information, i.e., mean and covariance matrix are known. For the problem, we develop a service-oriented distributionally robust optimization model. The objective is to maximize the service satisfaction, which is measured by the probability of completing the tasks on time. To solve it, the widely used sample average approximation (SAA) method is first adapted. However, the SAA method is time-consuming to the NP-hardness of the problem. Thus, by analyzing the characteristics of the problem, we propose a new method based on approximate mixed integer second-order cone programming (MI-SOCP). The efficiency and effectiveness of the proposed method are verified by the results of a real case as compared with the SAA method.