Real-time Approximate Routing for Smart Transit Systems

We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) seeks to serve set incoming trip requests. The can use its fleet as feeder connect passengers fleet, which operates on fixed routes. Our goal is find optimal (bus) routes corresponding frequencies maximize social welfare system given time window. This generalizes Line Planning Problem, widely studied topic transportation literature, for existing solutions are either heuristic (with no performance guarantees), require extensive computation (and hence impractical use). To this end, we develop 1-1/e-? approximation algorithm Real-Time using ideas from randomized rounding Generalized Assignment Problem. guarantee holds under two assumptions: (i) inter-bus transfers (ii) access pre-specified feasible bus lines. moreover show that these assumptions crucial by proving that, if assumption relaxed, ?ineplanningproblem does not admit any constant-factor approximation. Finally, demonstrate practicality our via numerical experiments real-world synthetic datasets, budget, outperforms Integer Linear Programming-based exact methods.