Department of Industrial Enginering & Decision Analytics [IEDA Seminar] - Parallel Queues with Match-Dependent Utility: Empirical Evidence and Asymptotic Characterization
We consider a parallel-queue system in which the customer's utility depends on the customer-server type matching and the arrival process is driven by a discrete choice model, that is, customers observe the queue length for each service provider and choose one to join upon arrival. We assume that a customer’s utility is different between the service reward and the waiting cost, both of which are heterogeneous. Empirical evidences of the vehicle queues at the U.S.-Canada border-crossing port of entry and the emergency departments in Hong Kong support our model setting. We show that with such a choice model, the arrival rate function satisfies certain properties, which allow us to characterizes the fluid and diffusion limit of the queue-length process. In particular, we show that even without the well-used Lipschitz-continuity assumption, the fluid limit process is unique and is attracted to a unique equilibrium. The diffusion limit process is a reflected multi-dimensional Ornstein-Uhlenbeck process centered at that equilibrium. We prove that the stationary distribution of the diffusion limit is a truncated multivariant Gaussian and interchange of limits holds.
Dr. Yichuan Ding is currently an associate professor in the Desautels Faculty of Management, McGill University. He has been honored as the Desautels Faculty Scholar. Dr. Ding currently serves as the director of the Management Sciences Research Center and the director of the Global Manufacturing and Supply Chain Management Program in the faculty. Dr. Ding obtained his PhD in management science and engineering from Stanford University. His research interests include optimization, queueing, and data analytics, as well as their applications in healthcare delivery systems, including emergency department operations, outpatient care, operation rooms, intensive care unit, and organ transplant. He has published on top-tier academic journals including operations research, mathematics of operations research, manufacturing and service operations management, and production and operations management. Dr. Ding was the winner of the 2023 POMS College of health care operations management best paper competition, the finalist of the 2019 Pierskalla Best Paper Competition, and the finalist of the 2017 INFORMS behavioural operations management best working paper competition. He currently serves as the associate editor for Manufacturing and Service Operations Management (M&SOM), Decision Sciences, and Operations Research Letters.