A Distributionally Robust Optimization for Reliability-Based Lane Reservation and Route Design Under Uncertainty

Lane reservation optimization is important in intelligent transportation systems. Most existing studies are carried out under deterministic road conditions by assuming constant road travel time. However, road conditions vary due to various factors, resulting in uncertain road travel time. This work addresses a new reliability-based lane reservation and route design problem by considering uncertain road travel time with its known mean and covariance matrix. It aims to decide which road segments in a network should implement reserved lanes and to design routes for special time-crucial transportation tasks. The objective is to maximize transportation service reliability (i.e., the probability of completing the special tasks on time). For this problem, a novel distributionally robust optimization model is first established. To solve it, this work proposes i) an adapted sample average approximation-based approach and ii) a two-stage hierarchical heuristic algorithm based on second-order cone programming. Experimental results on an illustrative example and a real-world case demonstrate that the latter is more effective and efficient than the former. In addition, we conduct a series of parameter sensitivity analysis experiments to reveal the factors affecting lane reservation and provide optimal solutions given different parameter settings.