Stochastic Modeling of Service-Time Distribution of a Shared Autonomous Vehicle Service

Autonomous vehicles (AVs) have paved the way for dynamic and intelligent forms of shared mobility that have the potential to revolutionize the transportation sector. The success of shared mobility, such as shared autonomous vehicles (SAVs), is highly dependent on their operational efficiency, however, and further study is needed to evaluate their overall performance. Thus, this study examines the productivity of an autonomous mobility-on-demand service operating in Arlington, Texas, using a queuing theory framework informed by upstream research on service-time distributions. A calibrated queuing model was employed and fitted to the data, and time-of-day curves were generated to evaluate two operational signals, which revealed instances in which the system was either bottlenecked or underutilized: the expected number of riders waiting for a ride and the expected number of idle vehicles. Additionally, the study characterized how the arrival rate of riders shaped expected waiting times within the calibrated M/E₇,4 framework, identifying a critical demand threshold beyond which congestion and queueing delays increase sharply. The results revealed clear demand peaks with higher wait times and a minimal number of idle vehicles during late afternoon hours, contrasted with reduced demand with lower wait times and more idle vehicles in the early morning hours. By integrating mobility behavior with stochastic modeling techniques, the study provides insight into the performance of a SAV service and recommends actionable outputs for optimizing its service that will benefit policymakers, service operators, and transportation professionals.