Algorithm for finding optimal paths in a public transit network with real-time data

Recently, transit agencies have been opening up their route configuration and schedule data to the public, as well as providing online APIs (Application Programming Interfaces) to real-time bus positions and arrival estimates. Based on this infrastructure of providing transit data over the internet, we developed an algorithm to calculate the travel times of K-shortest paths in a public transportation network where all wait and travel times are only known at real-time. Although there is a large body of work in routing algorithms in transit networks, we take cues from an algorithm to find shortest paths in road networks, called Transit Node routing. Our approach is based on a simple observation intuitively used by humans: when you take transit, you will look for a particular set of transfer points that connect transit routes that lead from the origin and destination. We precompute a lookup table of feasible paths between the origin stop of every bus route to the terminus of every other bus route using the transfer points. This precomputation of paths significantly reduces the computation time and number of real-time arrival requests to transit agency servers, the bottleneck in computing this problem. The computational complexity of the algorithm is linear in real-time and implementation results show that queries from a webserver are returned in 3 seconds in the worst-case.