Simple Rules for Predicting Congestion Risk in Queueing Systems: Application to ICUs

50 Pages Posted: 15 May 2019 Last revised: 7 Aug 2020

See all articles by Fernanda Bravo

Fernanda Bravo

University of California, Los Angeles (UCLA) - Anderson School of Management

Cynthia Rudin

Duke University - Pratt School of Engineering; Duke University

Yaron Shaposhnik

University of Rochester - Simon Business School

Yuting Yuan

University of Rochester - Simon Business School

Date Written: May 7, 2019

Abstract

We study the problem of predicting congestion risk in service systems, a factor associated with poor service experience, higher costs, and even medical risk (e.g., in ICUs). By predicting future congestion, decision- makers can initiate preventive measures such as rescheduling activities or increasing short-term capacities in order to mitigate the effects of congestion. To this end, we define “high-risk states” in queuing models as system states that are likely to lead to a congested state in the near future, and strive to formulate simple rules for determining whether a given system state is high-risk. We show that for simple queueing systems, such as the M / M / ∞ queue with multiple user classes, such rules could be approximated by linear and quadratic functions on the state space. For more general queueing systems, we employ methods from queueing theory, simulation, and machine learning (ML) to devise simple prediction rules, and demonstrate their effectiveness through extensive computational study, which includes a large scale ICU model validated using data. Our study suggests combining custom model-based interpretable features with linear models (which are widely considered to be interpretable) can accurately predict congestion in ICUs.

Keywords: Congestion; Queueing systems; Prediction; Service operation; Machine learning; Interpretability; ICU

Suggested Citation

Bravo, Fernanda and Rudin, Cynthia and Shaposhnik, Yaron and Yuan, Yuting, Simple Rules for Predicting Congestion Risk in Queueing Systems: Application to ICUs (May 7, 2019). Available at SSRN: https://ssrn.com/abstract=3384148 or http://dx.doi.org/10.2139/ssrn.3384148

Fernanda Bravo

University of California, Los Angeles (UCLA) - Anderson School of Management ( email )

110 Westwood Plaza
Los Angeles, CA 90095-1481
United States

Cynthia Rudin

Duke University - Pratt School of Engineering ( email )

Durham, NC 27708
United States

Duke University ( email )

Department of Computer Science
LSRC Building
Durham, NC 27708-0204
United States

Yaron Shaposhnik

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

Yuting Yuan (Contact Author)

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

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