On the Tracking of Dynamical Optimal Meeting Points

Finding optimal meeting points on road networks is becoming more and more relevant with the growth of ride-sharing services. Optimal meeting points serve as locations where multiple vehicles can drop their passengers, which will then be pooled in one single (high capacity) vehicle to reach their common final destination. Finding good meeting points is then key in ensuring low travel times to the chosen location and therefore high quality of service. Optimal meeting points are hardy stationary, since variations on traffic conditions, road events, or drivers predispositions to go slower/faster than predicted could shift optimality from one location to another one continuously in time. In this paper, we propose online algorithms to find and track optimal meeting points in such dynamic scenarios, as well as a system architecture to enable extensive simulations for any selected network of interest. Our algorithms are an extension of existing static algorithms. First we integrate realistic considerations such as the finite number of drop-off locations and the proximity radius constant to avoid constant rerouting of vehicles. Second we adapt those algorithms to the dynamic case, which requires to address the trade-off between computational time and optimality. With the aid of extensive numerical simulations, we illustrate and discuss the effectiveness of each algorithm under different scenarios: static networks, dynamic congested networks and dynamic congested network subject to dynamic events.