Mainstream queueing models are frequently employed in modeling healthcare delivery in a number of settings, and further are used in making operational decisions for the same. The vast majority of these queueing models ignore the effects of delay experienced by a patient awaiting care. However, 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. This work sets out to understand these delay issues from an operational perspective. Using data of over 57,000 Emergency Department (ED) visits, we use an instrumental variable approach to empirically measure the impact of delays in ICU admission, i.e. ED boarding, on the patient’s ICU LOS for multiple patient types.
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. We propose a queueing model which incorporates these measured delay effects and characterize approximations to the expected work in the system when the service time of a job is adversely impacted by the delay experienced by that job. Our approximation demonstrates an effect of system load on work which grows much faster than the traditional 1/(1 − ρ) relationship seen in most queueing systems. As such, it is imperative that the relationship of delays on LOS be better understood by hospital managers so that they can make capacity decisions that prevent even seemingly moderate delays from causing dire operational consequences.