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Ride hailing (RH) services have become a common mode of transportation in the last decade. Usually, statistical tools are used to improve their performance, whereby the tools typically divide the whole operational area into multiple regions. These tools usually assume that the regions are independent of each other even though vehicles from one region can be used to serve neighboring regions, thereby a method is required that consistently relates vehicle demand and supply between geographically neighboring regions or to the whole operating area. This hinders tapping into the full potential of region-based performance improvement techniques like the repositioning of idle vehicles. Therefore, we develop an innovative reachability function-based method that coherently builds a relation among all regions in the form of a spatial density of the measured quantity. We use it to calculate the differences of vehicle supply and demand for the whole operational area in the form of an imbalance density. Based on this, we derive a novel repositioning formulation that significantly reduces both the overall vehicle imbalances and the total distance of repositioning trips, and thus improves the long-term RH performance. We test the approach in an agent-based simulation for an RH scenario with automated vehicles, using open-source New York City taxi data as demand. The approach shows a remarkable improvement over the state of the art repositioning strategies that balance the fleet over the individual regions. Furthermore, we introduce kernel-based key performance indicators (KPIs) that can be calculated at the time of making repositioning decisions. We also show the correlation of the KPIs with long-term performance gains. We expect that these KPIs can benefit future statistical (machine learning) approaches for repositioning.

Density Based Distribution Model for Repositioning Strategies of Ride Hailing Services