Capacity Scaling for Observable Queues

30 Pages Posted: 16 Jun 2020 Last revised: 31 May 2024

See all articles by Yang Li

Yang Li

University of Western Ontario - Richard Ivey School of Business

Daniel Zhuoyu Long

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management

Rowan Wang

Southern University of Science and Technology - School of Business

Zijin Zhang

University of Michigan, Stephen M. Ross School of Business

Date Written: June 14, 2020

Abstract

Problem definition: This study aims to understand the benefits and drawbacks of scaling a queueing system incorporating people's balking behavior. Methodology/results: We collected extensive data on real-time queue status from thousands of testing sites in China. Our findings reveal that the principle of economies of scale does not always apply. Specifically, when demand falls below service capacity, scaling up systems demonstrates shorter waiting time; however, when demand exceeds service capacity, larger systems unexpectedly experience longer waiting. Motivated by these empirical insights, we build classic queueing models to analytically characterize how system performance measures, including expected waiting time, queue length, balking probability, and social welfare, change with system size across different levels of utilization. In alignment with our empirical findings, our analytical results show that under low utilization, scaling systems can decrease waiting time and balking probability, improve social welfare, although queue length will increase but up to a limit; under high utilization, scaling systems increases waiting time and queue length and results in lower social welfare, while balking rate continues to decrease. Managerial implications: Understanding that scaling queueing systems may not always improve performance, managers should carefully adopt strategies based on demand patterns and service capacity in order to prevent situations where scaling worsens system performance in queueing environments.

Keywords: observable queues, balking, delay sensitive, capacity scaling, service management

Suggested Citation

Li, Yang and Long, Daniel Zhuoyu and Wang, Rowan and Zhang, Zijin, Capacity Scaling for Observable Queues (June 14, 2020). Available at SSRN: https://ssrn.com/abstract=3628484 or http://dx.doi.org/10.2139/ssrn.3628484

Yang Li

University of Western Ontario - Richard Ivey School of Business ( email )

1151 Richmond Street North
London, Ontario N6A 3K7
Canada

Daniel Zhuoyu Long (Contact Author)

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management ( email )

Hong Kong
China

Rowan Wang

Southern University of Science and Technology - School of Business ( email )

China

Zijin Zhang

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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