Control of Patient Flow in Emergency Departments, or Multiclass Queues with Deadlines and Feedback

Abstract

We consider the control of patient flow through physicians in emergency departments (EDs). The physicians must choose between catering to patients right after triage, who are yet to be checked, and those that are in-process (IP), who are occasionally returning to be checked. Physician capacity is thus modeled as a queueing system with multiclass customers, where some of the classes face deadline constraints on their time-till-first-service, while the other classes feedback through service while incurring congestion costs. We consider two types of such costs: first, costs that are incurred at queue-dependent rates, and second, costs that are functions of IP sojourn time. The former is our base-model, which paves the way for the latter (perhaps more ED-realistic). In both cases, we propose and analyze scheduling policies that, asymptotically in conventional heavy-traffic, minimize congestion costs while adhering to all deadline constraints. Our policies have two parts: the first chooses between triage and IP patients; assuming triage patients are chosen, the physicians serve the one who is closest to violating the deadline; alternatively, IP patients are served according to a Gcµ rule, in which µ is simply modified to account for feedbacks. For our proposed policies, we establish asymptotic optimality, and develop some congestion laws (snapshot principles) that support forecasting of waiting and sojourn times. Simulation then shows that these policies outperform some commonly-used ones. It also validates our laws and demonstrates that some ED features, the complexity of which reaches beyond our model (e.g., time-varying arrival rates, Leave-Without-Being-Seen (LWBS) or Leave-Against-Medical-Advice (LAMA)), do not lead to significant performance degradation.

Operations research/management contributions to emergency department patient flow optimization: Review and research prospects

“…Queueing Theory has also been applied as an extension to the Maximum Availability Location Problem (MALP), where it is used to relax the assumption that server availability is independent (Marianov and ReVelle, 1996;Ghani, 2012). Huang (2013) and Huang et al (2013) split patients into two queueing networks, new patients and WIP patients, to optimize physician decisions of which patients to service. Gallivan et al (2002) simplify the patient flow process through a heavy-traffic deterministic system, assuming that the number of patients per day, the probability of "success," and patient LOS is always the same.…”

“…Time and motion studies were also among pioneers to identify issues with ED patient flow (Heckerling, 1985;Saunders, 1987). More modern techniques can be found in studies such as Green (2006), Green et al (2006), ), Saghafian et al (2012, 2014, Huang (2013), Huang et al (2013), and many others that we will review. In reviewing such studies, we hope to provide a resource for both researchers and practitioners to familiarize them with past related, valuable contributions, and to invoke to plan future studies that can help EDs reach new levels of both operational efficiency and patient safety.…”

Analysis of a Hierarchical Structured Queuing System With Three Service Channels, and Chances of Repetition of Service With Feedback

“…A large number of researchers have done a lot of work on queuing models considering various aspects such as bulk service, impatient customers, cyclic queues, batch arrivals, reneging, blocking. Study on queuing models considering the concept of feedback has also been done by a large number of researchers including Kumar (1990), Garg and Kumari (1998), Garg and Srivastava (2006), Kusum (2010), Huang et al (2015), Raheja et al (2016). Kusum et al (2010) discussed queues with feedback wherein three servers have been considered wherein a customer may go back to his/her preceding service channel or moving forward to immediate next service channel, except from the third server.…”

Managing urgent care in hospitals

“…Alternative patient pathways and policies assigning non-elective patients to these pathways are also investigated [104]. Finally, patient (time dependent) prioritization rules are also investigated [111,164,173,232], and tools to assist the triage patient categorization that provide further guidelines for patient selection [72].…”

“…Comparing the triage policies with existing systems (i.e., ESI) they find that length of stay at the ED, and the percentage of patients past their waiting time is reduced. [111] use queuing theory to model patient flow through an ED and formulate policies that determine which patients physicians treat next (i.e., triage new patients or treat 'in process' patients). They find an optimal policy that minimizes congestion of the ED under heavy traffic.…”