Service-oriented distributionally robust lane reservation

Abstract

Most existing lane reservation studies usually consider a static transportation network with assuming constant link travel times. However, in reality the link travel times are highly uncertain due to various factors such as weather, accidents, road maintenance, intersections, etc. Moreover, the precise link travel time probability distribution is usually difficult to be obtained. This paper studies a new stochastic bus lane reservation problem with partial link travel time information, i.e., only the mean and covariance matrix are known. The objective is to maximize the bus service level measured by the probability of the event that all lines are jointly scheduled on time. For the problem, we formulate a service-oriented distributionally robust optimization model. Its complexity is shown to be NP-hard. To solve the problem, a sample average approximation (SAA)-based method is first adapted. Since the SAA-based approach is computational expensive, a new approximated mixed integer second-order cone programming (MI-SOCP)-based approach is developed. Computational results on a real-life case show that the proposed MI-SOCP-based approach can efficiently obtain satisfactory solutions of high quality. Besides, our results indicate that the proposed model and algorithm can provide better solutions with higher service level, as compared with general stochastic models with known distributions and without considering service levels.