Robust Line Planning in case of Multiple Pools and Disruptions

We consider the line planning problem in public transportation, under a robustness perspective. We present a mechanism for robust line planning in the case of multiple line pools, when the line operators have a different utility function per pool. We conduct an experimental study of our mechanism on both synthetic and real-world data that shows fast convergence to the optimum. We also explore a wide range of scenarios, varying from an arbitrary initial state (to be solved) to small disruptions in a previously optimal solution (to be recovered). Our experiments with the latter scenario show that our mechanism can be used as an online recovery scheme causing the system to re-converge to its optimum extremely fast.Comment: To appear in TAPAS 201

The line planning routing game

In this paper, we propose a novel algorithmic approach to solve line planning problems. To this end, we model the line planning problem as a game where the passengers are players which aim at minimizing individual objective functions composed of travel time, transfer penalties, and a share of the overall cost of the solution. To find equilibria of this routing game, we use a best-response algorithm. We investigate, under which conditions on the line planning model a passenger’s best-response can be calculated efficiently and which properties are needed to guarantee convergence of the best-response algorithm. Furthermore, we determine the price of anarchy which bounds the objective value of an equilibrium with respect to a system- optimal solution of the line planning problem. For problems where best-responses cannot be found efficiently, we propose heuristic methods. We demonstrate our findings on some small computational examples