Finding Reliable Paths Considering the Earliest Arrival Time and the Latest Departure Time With 3-Parameter Lognormal Travel Times

Due to the influence of various factors, travel time is highly dynamic and random, causing late arrival and imposing a high penalty on travelers. To ensure punctual arrival, this paper presents two models and algorithms to find reliable paths considering the earliest arrival time and the latest departure time. First, the 3-parameter lognormal (3P-LN) distribution is introduced to describe travel time. Next, an optimality condition based on travel time bounds is derived and established when travel time follows the 3P-LN distribution. Then, a reliable path model considering the earliest arrival time and the solution algorithm based on travel time bounds are proposed to find the earliest arrival time and the corresponding reliable path. After that, a reliable path model considering the latest departure time and the solution algorithm based on travel time bounds are developed to find the latest departure time and the corresponding reliable path. Finally, two case studies with a real-world road network in Beijing are conducted to verify the effectiveness and superiority of the proposed models and algorithms.