In this talk, we present two applications of fluid models derived as limit processes. The first application is in reliability, focusing on a selective maintenance problem for large-scale systems consisting of many identical units that independently follow non-Markovian multi-state degradation processes. This problem is motivated by the maintenance of large-scale wind farms, where a single maintenance trip cannot cover all units due to the scale of the system. We use a fluid model to describe the system dynamics and propose a threshold-type maintenance policy that minimizes costs. The second application is in queueing theory, addressing the overlapping times of customers, motivated by the COVID-19 pandemic. Longer overlapping times among customers may increase potential infection risks. We propose a new performance measure, overlapping time, in addition to traditional measures such as queue lengths and waiting times, and we analyze it in time-varying queueing systems. Unlike previous studies that establish almost sure convergence and use it as an approximation for the mean value, we show L1 convergence, which directly relates to the mean overlapping times.

Young Myoung Ko is a Professor of Industrial & Management Engineering at Pohang University of Science and Technology (POSTECH), where he currently serves as Department Head. He received his bachelor’s and master’s degrees from Seoul National University and his Ph.D. from Texas A&M University. His research interests include queueing theory and its applications, as well as maintenance optimization for large-scale systems. Recently, he has been developing data-driven approaches such as queueing-informed machine learning and optimization under uncertainty using pre-trained foundation models.