The Impact of Delays on Service Times in the Intensive Care Unit

Abstract

Mainstream queueing models are frequently employed in modeling healthcare delivery in a number of settings, and further used in making operational decisions for the same. The vast majority of these queueing models assume that the service requirements of a job are independent of the state of the queue upon its arrival. In a healthcare setting, this assumption is equivalent to ignoring the effects of delay experienced by a patient awaiting care. However, it is only natural to conjecture that long delays may have adverse effects on patient outcomes and can potentially lead to longer lengths of stay (LOS) when the patient ultimately does receive care. At a very coarse level, prior research confirms these natural conjectures. This work sets out to understand these delay issues from an operational perspective. In particular, using data of nearly 6,000 Emergency Department (ED) visits, we use an instrumental variable approach to empirically measure how congestion in the Intensive Care Unit (ICU) can lead to delays in boarding from the ED to the ICU and measure the impact on the patient's ICU LOS.Capturing these empirically observed effects in a queueing model is challenging as the effect introduces potentially long range correlations in service and inter-arrival times. As such, we consider the problem of how to incorporate these measured delay effects into a queueing model and characterize approximations to various quantities of interest when the service time of a job is adversely impacted by the delay experienced by that job. Our findings suggest that this delay effect can be substantial and ignoring it when using queueing models to model healthcare delivery systems may result in significant under-provisioning.

Critical Care Capacity Management: Understanding the Role of a Step Down Unit

“…We set the probability of return to critical and semi‐critical , which is similar to the rates given in Chan et al. (). Based on estimates from personal communication with medical professionals, we set θ = 1 so that patients can tolerate waits of 1 day on average and x = 1.5 so that treating critical patients in the SDU takes 50% as long as in the ICU.…”

The snowball effect of customer slowdown in critical many-server systems

“…We shall adopt the model in [8], which is a multi-server model with a threshold service rate function µ(·). Customers arrive according to a Poisson process with rate λ, have an exponential service requirement, and are served by s servers.…”

“…In [8], approximations are derived for key performance indicators that give insight into the slowdown effect. Based on parameter values calibrated from real ICU dataflows, the approximations in [8] indicate that the slowdown effect can be substantial, and should not be ignored in critical care systems that operate in heavy traffic. This two-dimensional Markov process can be used to investigate the impact of slowdown, both qualitatively and quantitatively, in particular in comparison with the widely applied M/M/s system (which neglects slowdown).…”

“…A canonical example in this domain is the admission of patients to the intensive care unit (ICU). There is substantial empirical evidence for slowdown in such settings: delays in receiving appropriate care can result in adverse effects such as an increased length of stay in the ICU [7,8,9,22,23,24]. Since ICUs are typically heavily used and subject to unforeseen circumstances, delays in admitting patients are the rule rather than the exception, which makes the slowdown effect potentially threatening.…”

Clearing analysis on phases: Exact limiting probabilities for skip-free, unidirectional, quasi-birth-death processes

“…Of course, there are many systems beyond those covered in this section that can be modeled by class M Markov chains. For example, class M chains were recently used to model medical service systems in [8], [5], and [25].…”