Parallel Queues with Discrete-Choice Arrival Pattern: Empirical Evidence and Asymptotic Characterization

Abstract

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 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.