Rebalancing the Rebalancers: Optimally Routing Vehicles and Drivers in Mobility-on-Demand Systems

TL;DR

This paper develops an optimal routing strategy for rebalancing vehicles and drivers in a mobility-on-demand system, ensuring system stability while minimizing rebalancing resources through decoupled linear programs.

Contribution

It introduces a novel approach to simultaneously optimize vehicle and driver rebalancing by solving two decoupled linear programs, ensuring stability with minimal resources.

Findings

Optimal rebalancing strategies can be obtained via linear programming.

The number of drivers needed is roughly 25-33% of the number of vehicles.

Simulations confirm the efficiency of the proposed approach in Euclidean networks.

Abstract

In this paper we study rebalancing strategies for a mobility-on-demand urban transportation system blending customer-driven vehicles with a taxi service. In our system, a customer arrives at one of many designated stations and is transported to any other designated station, either by driving themselves, or by being driven by an employed driver. The system allows for one-way trips, so that customers do not have to return to their origin. When some origins and destinations are more popular than others, vehicles will become unbalanced, accumulating at some stations and becoming depleted at others. This problem is addressed by employing rebalancing drivers to drive vehicles from the popular destinations to the unpopular destinations. However, with this approach the rebalancing drivers themselves become unbalanced, and we need to "rebalance the rebalancers" by letting them travel back to the popular destinations with a customer. Accordingly, in this paper we study how to optimally route the rebalancing vehicles and drivers so that stability (in terms of boundedness of the number of waiting customers) is ensured while minimizing the number of rebalancing vehicles traveling in the network and the number of rebalancing drivers needed; surprisingly, these two objectives are aligned, and one can find the optimal rebalancing strategy by solving two decoupled linear programs. Leveraging our analysis, we determine the minimum number of drivers and minimum number of vehicles needed to ensure stability in the system. Interestingly, our simulations suggest that, in Euclidean network topologies, one would need between 1/3 and 1/4 as many drivers as vehicles.