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

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.