Collective dynamics of capacity-constrained ride-pooling fleets

TL;DR

This paper develops a theoretical framework to understand how capacity constraints affect the efficiency and dynamics of ride-pooling fleets, extending existing scaling laws to more realistic scenarios.

Contribution

It introduces an effective fleet size concept and generalizes scaling laws for ride-pooling efficiency considering capacity constraints.

Findings

Scaling laws hold for capacity-constrained fleets when using an effective fleet size.

Queueing theory approximates the dynamics and predicts fleet size requirements.

The model aids transfer of insights across different ride-pooling service settings.

Abstract

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.