Estimating Real Demand Using a Flipped Queueing Model: A Case of Shared Micro-Mobility Services

Abstract

The spatial-temporal imbalance between supply and demand in shared micro-mobility services often leads to observed demand being censored, resulting in incomplete records of the underlying real demand. This phenomenon undermines the reliability of the collected demand data and hampers downstream applications such as demand forecasting, fleet management, and micro-mobility planning. How to accurately estimate the real demand is challenging and has not been well explored in existing studies. In view of this, we contribute to real demand estimation for shared micro-mobility services by proposing an analytical method that rigorously derives the real demand under appropriate assumptions. Rather than directly modeling the intractable relationship between observed demand and real demand, we propose a novel random variable, Generalized Vehicle Survival Time (GVST), which is observable from trip records. The relationship between GVST and real demand is characterized by introducing a flipped queueing model (FQM) that captures the operational dynamics of shared micro-mobility services. Specifically, the distribution of GVST is derived within the FQM, which allows the real demand estimation problem to be transformed into an inverse queueing problem. We analytically derive the real demand in closed form using a one-sided estimation method, and solve the problem by a system of equations in a two-sided estimation method. We validate the proposed methods using synthetic data and conduct empirical analyses using real-world datasets from bike-sharing and shared e-scooter systems. The experimental results show that both the two-sided and one-sided methods outperform benchmark models. In particular, the one-sided approach provides a closed-form solution that delivers acceptable accuracy, constituting a practical rule of thumb for demand-related analytics and decision-making processes.