Mean-Field Control of Adherence in Participation-Coupled Vehicle Rebalancing Systems

TL;DR

This paper models driver participation in MoD systems as a stochastic process, deriving a mean-field recursion to optimize platform recommendations balancing adherence and throughput.

Contribution

It introduces a microscopic stochastic model coupling participation beliefs, demand, and matching, with a mean-field analysis for optimal platform recommendation strategies.

Findings

Proves global well-posedness and convergence of the mean-field recursion.

Characterizes the performance frontier between adherence and throughput.

Provides an efficient algorithm for optimal recommendation intensity.

Abstract

Human driver participation is a critical source of uncertainty in Mobility-on-Demand (MoD) rebalancing. Drivers follow platform recommendations probabilistically, and their willingness to comply evolves with experienced outcomes. This creates a closed-loop feedback in which stronger recommendations increase participation, participation increases congestion, congestion lowers allocation success, and realized allocations update adherence beliefs. We propose a microscopic stochastic model that couples (i) belief-driven participation, (ii) Poisson demand, (iii) uniform matching, and (iv) Beta--Bernoulli belief updates. Under a large-population closure, we derive a deterministic mean-field recursion for the population adherence state under platform actuation. For i.i.d. Poisson demand and constant recommendation intensity, we prove global well-posedness and invariance of the recursion, establish equilibrium existence, provide uniqueness conditions, and show global convergence in the regime where platform recommendations are no weaker than baseline participation. We then define steady-state adherence and throughput, characterize the induced performance frontier, and show that adherence and throughput cannot, in general, be simultaneously maximized under uniform time-invariant actuation. This yields a throughput-maximization problem with an adherence floor. Exploiting the monotone frontier structure, we show the optimal uniform time-invariant policy is the maximal feasible recommendation intensity and provide an efficient bisection-based algorithm.