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

53 Pages Posted: 21 May 2020

See all articles by Yichuan Ding

Yichuan Ding

Desautels Faculty of Management, McGill University

Mahesh Nagarajan

University of British Columbia (UBC) - Sauder School of Business

George Zhang

affiliation not provided to SSRN

Date Written: April 25, 2020

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.

Keywords: Discrete Choice Model, Nonlinear Complementarity Problem, Fluid and Diffusion Approximation, Reflected Multi-Dimensional Ornstein-Uhlenbeck Process

Suggested Citation

Ding, Yichuan and Nagarajan, Mahesh and Zhang, George, Parallel Queues with Discrete-Choice Arrival Pattern: Empirical Evidence and Asymptotic Characterization (April 25, 2020). Available at SSRN: https://ssrn.com/abstract=3584880 or http://dx.doi.org/10.2139/ssrn.3584880

Yichuan Ding (Contact Author)

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrook St W
Montreal, Quebec H3A 1G5
Canada
5143982482 (Phone)

HOME PAGE: http://https://www.mcgill.ca/desautels/yichuan-daniel-ding

Mahesh Nagarajan

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

George Zhang

affiliation not provided to SSRN ( email )

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