A linear program for optimal integration of shared autonomous vehicles with public transit

Use of shared autonomous vehicles (SAVs) for last-mile transportation can improve transit use and reduce road congestion. We investigate the problem of optimal integration of SAVs with transit. By optimal, we mean that transit should be used instead of or to complement SAVs only when it reduces the total system travel time. Although greater use of transit reduces congestion, transit often increases travel time due to frequent stops and transfers. By using a continuous approximation to passenger and vehicle movements, we formulate the problem as a linear program using the link transmission model for traffic flow. One of the main challenges is associating passenger movement with vehicles that can have different destinations (e.g. a transit stop). Although the mathematical program is linear, it nevertheless has a large number of variables. We find a suboptimal solution using a rolling horizon method, which greatly reduces the required computation time. We also demonstrate an example of a possibly unfair passenger-to-vehicle ordering, and propose a first-come-first-served greedy algorithm to match passengers. A suite of experimental results on the Sioux Falls network show that using transit decreases total system travel time, especially when SAV fleet sizes are small. Transit also decreases the time travelers spend waiting, but tends to increase in-vehicle travel time. The methodology could be useful both for future SAV operators and for planners seeking to predict the effects of SAVs on traffic congestion.