讲座题目：Parallel Queues with Discrete-Choice Arrival Pattern: Empirical Evidence and Asymptotic Characterization
We consider a parallel-queue system in which each queue is served by a dedicated service provider. 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 difference between the service reward and the waiting cost, both of which are heterogeneous. Empirical analysis of the vehicle queues at the U.S.-Canada border-crossing port of entry supports our model setting. We show that with such a choice model, the arrival rate function satisfies certain properties, which allow us to characterize 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
Yichuan Ding is currently anassociateprofessor, Desautels Faculty Scholar in the Desautels Faculty of Management, McGill University. He is currently the director of Management Sciences Research Center and the Global Manufacturing and Supply Chain Management Program. He obtained his PhD from Stanford University in 2012. His research interests include optimization, queueing, and data analytics, as well as their applications in public sectors, including cadaver kidney exchange and allocation policies, affordable housing management, emergency department operations, outpatient and surgical scheduling, etc. He has published on top-tier academic journals includingoperations research, mathematics of operations research, manufacturing and service operations management.Heis currently the associate editor formanufacturing and service operations management, decision sciences, and operations research letters.