Service Systems with Dependent Service and Patience Times

Management Science, Forthcoming

39 Pages Posted: 10 Jan 2017 Last revised: 12 Oct 2017

See all articles by Chenguang (Allen) Wu

Chenguang (Allen) Wu

Hong Kong University of Science and Technology

Achal Bassamboo

Northwestern University - Department of Managerial Economics and Decision Sciences (MEDS)

Ohad Perry

Northwestern University - Department of Industrial Engineering and Management Sciences

Date Written: January 7, 2017

Abstract

Motivated by recent empirical evidence, we consider a large service system in which the patience time of each customer depends on his service requirement. Our goal is to study the impact of such dependence on key performance measures, such as expected waiting times and average queue length, as well as on optimal capacity decisions. Since the dependence structure renders exact analysis intractable, we employ a stationary fluid approximation that is based on the entire joint distribution of the service and patience times. Our results show that even moderate dependence has significant impacts on system performance, so considering the patience and service times to be independent when they are in fact dependent is futile. We further demonstrate that Pearson’s correlation coefficient, which is commonly used to measure and rank dependence, is an insufficient statistic, and that the entire joint distribution is required for comparative statics. Thus, we propose a novel framework, incorporating the fluid model with bivariate dependence orders and copulas, to study the impacts of the aforementioned dependence. We then demonstrate how that framework can be applied to facilitate revenue optimization when staffing and abandonment costs are incurred. Finally, the effectiveness of the fluid-based approximations and optimal-staffing prescriptions is demonstrated via simulations.

Keywords: Service Systems, Dependence, Fluid Approximation, Bivariate Dependence Order, Copulas, Capacity Sizing

Suggested Citation

Wu, Chenguang (Allen) and Bassamboo, Achal and Perry, Ohad, Service Systems with Dependent Service and Patience Times (January 7, 2017). Management Science, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2895413 or http://dx.doi.org/10.2139/ssrn.2895413

Chenguang (Allen) Wu (Contact Author)

Hong Kong University of Science and Technology ( email )

Room 5559C, Academic Building
HongKong University of Science and Technology
Hong Kong
Hong Kong

Achal Bassamboo

Northwestern University - Department of Managerial Economics and Decision Sciences (MEDS) ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Ohad Perry

Northwestern University - Department of Industrial Engineering and Management Sciences ( email )

2145 Sheridan Road
Room C210
Evanston, IL 60208
United States

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