A Queue-Based Monte Carlo Analysis to Support Decision Making for Implementation of an Emergency Department Fast Track

Obstetric operating room staffing and operating efficiency using queueing theory

INTRODUCTION

Strategies to achieve efficiency in non-operating room locations have been described, but emergencies and competing priorities in a birth unit can make setting optimal staffing and operation benchmarks challenging. This study used Queuing Theory Analysis (QTA) to identify optimal birth center operating room (OR) and staffing resources using real-world data.

METHODS

Data from a Level 4 Maternity Center (9,626 births/year, cesarean delivery (CD) rate 32%) were abstracted for all labor and delivery operating room activity from July 2019-June 2020. QTA has two variables: Mean Arrival Rate, λ and Mean Service Rate µ. QTA formulas computed probabilities: P0 = 1-(λ/ µ) and Pn = P0 (λ/µ)n where n = number of patients. P0…n is the probability there are zero patients in the queue at a given time. Multiphase multichannel analysis was used to gain insights on optimal staff and space utilization assuming a priori safety parameters (i.e., 30 min decision to incision in unscheduled CD; ≤ 5 min for emergent CD; no greater than 8 h for nil per os time). To achieve these safety targets, a < 0.5% probability that a patient would need to wait was assumed.

RESULTS

There were 4,017 total activities in the operating room and 3,092 CD in the study period. Arrival rate λ was 0.45 (patients per hour) at peak hours 07:00-19:00 while λ was 0.34 over all 24 h. The service rate per OR team (µ) was 0.87 (patients per hour) regardless of peak or overall hours. The number of server teams (s) dedicated to OR activity was varied between two and five. Over 24 h, the probability of no patients in the system was P0 = 0.61, while the probability of 1 patient in the system was P1 = 0.23, and the probability of 2 or more patients in the system was P≥2 = 0.05 (P3 = 0.006). However, between peak hours 07:00-19:00, λ was 0.45, µ was 0.87, s was 3, P0 was 0.48; P1 was 0.25; and P≥2 was 0.07 (P3 = 0.01, P4 = 0.002, P5 = 0.0003).

CONCLUSION

QTA is a useful tool to inform birth center OR efficiency while upholding assumed safety standards and factoring peaks and troughs of daily activity. Our findings suggest QTA is feasible to guide staffing for maternity centers of all volumes through varying model parameters. QTA can inform individual hospital-level decisions in setting staffing and space requirements to achieve safe and efficient maternity perioperative care.

An operations research approach to automated patient scheduling for eye care using a multi-criteria decision support tool

Inefficient management of resources and waiting lists for high-risk ophthalmology patients can contribute to sight loss. The aim was to develop a decision support tool which determines an optimal patient schedule for ophthalmology patients. Our approach considers available booking slots as well as patient-specific factors. Using standard software (Microsoft Excel and OpenSolver), an operations research approach was used to formulate a mathematical model. Given a set of patients and clinic capacities, the model objective was to schedule patients efficiently depending on eyecare measure risk factors, referral-to-treatment times and targets, patient locations and slot availabilities over a pre-defined planning horizon. Our decision support tool can feedback whether or not a patient is scheduled. If a patient is scheduled, the tool determines the optimal date and location to book the patients' appointments, with a score provided to show the associated value of the decisions made. Our dataset from 519 patients showed optimal prioritization based on location, risk of serious vision loss/damage and the referral-to-treatment time. Given the constraints of available slots, managers can input hospital-specific parameters such as demand and capacity into our model. The model can be applied and implemented immediately, without the need for additional software, to generate an optimized patient schedule.

Queueing Theory and COVID-19 Prevention: Model Proposal to Maximize Safety and Performance of Vaccination Sites

Introduction

COVID-19 (Coronavirus Disease 19) has rapidly spread all around the world. Vaccination represents one of the most promising counter-pandemic measures. There is still little specific evidence in literature on how to safely and effectively program access and flow through specific healthcare settings to avoid overcrowding in order to prevent SARS-CoV-2 transmission. Literature regarding appointment scheduling in healthcare is vast. Unpunctuality however, especially when targeting healthcare workers during working hours, is always possible. Therefore, when determining how many subjects to book, using a linear method assuming perfect adhesion to scheduled time could lead to organizational problems.

Methods

This study proposes a "Queuing theory" based approach. A COVID-19 vaccination site targeting healthcare workers based in a teaching hospital in Rome was studied to determine real-life arrival rate variability. Three simulations using Queueing theory were performed.

Results

Queueing theory application reduced subjects queueing over maximum safety requirements by 112 in a real-life based vaccination setting, by 483 in a double-sized setting and by 750 in a mass vaccination model compared with a linear approach. In the 3 settings, respectively, the percentage of station's time utilization was 98.6, 99.4 and 99.8%, while the average waiting time was 27.2, 33.84, and 33.84 min.

Conclusions

Queueing theory has already been applied in healthcare. This study, in line with recent literature developments, proposes the adoption of a Queueing theory base approach to vaccination sites modeling, during the COVID-19 pandemic, as this tool enables to quantify ahead of time the outcome of organizational choices on both safety and performance of vaccination sites.

Toward Building Surge Capacity: Potentially Effective Spatial Configurations in Emergency Departments

BACKGROUND

Emergency departments (EDs) have been struggling with overcrowding issues for years. Some spatial configurations have been proposed to improve ED performance in facing overcrowding. Despite similarities with mass casualty incidents (MCIs), when demand for care exceeds the capacity, little is documented about the application of the proposed configurations during MCIs to improve surge capacity.

OBJECTIVES

We aimed to explore the potential of spatial configurations that have been proposed to handle ED overcrowding in daily operations so as to improve surge capacity during MCIs.

METHODS

Using an online Likert-scale survey, 11 spatial design strategies were rated by ED care teams in terms of their potential to improve surge capacity during MCIs.

RESULTS

Responses from 72 participants revealed that establishing an in-house lab was perceived as the most potential strategy, followed by rapid care area, internal waiting rooms, and in-house imaging. In contrast, separate entrance and exit doors, as well as decentralized nurse stations, were perceived as the least potential strategies but also exhibited the most variance in response. Respondents' comments implied that their choice of in-house ancillary services was primarily to improve communication and to reduce turnaround time and risk of errors. Their choice of rapid care and internal waiting areas related to improved flexibility.

CONCLUSIONS

Understanding clinicians' perspectives on potentially effective spatial configurations aids in implementing balanced strategies to better equip EDs to handle overcrowding in daily operations and manage surges during MCIs.

Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies

Problems related to patient scheduling and queueing in emergency departments are gaining increasing attention in theory, in the fields of operations research and emergency and healthcare services, and in practice. This paper aims to provide an extensive review of studies addressing queueing-related problems explicitly related to emergency departments. We have reviewed 229 articles and books spanning seven decades and have sought to organize the information they contain in a manner that is accessible and useful to researchers seeking to gain knowledge on specific aspects of such problems. We begin by presenting a historical overview of applications of queueing theory to healthcare-related problems. We subsequently elaborate on managerial approaches used to enhance efficiency in emergency departments. These approaches include bed management, fast-track, dynamic resource allocation, grouping/prioritization of patients, and triage approaches. Finally, we discuss scientific methodologies used to analyze and optimize these approaches: algorithms, priority models, queueing models, simulation, and statistical approaches.

Specifications of a Queuing Model-Driven Decision Support System for Predicting the Healthcare Performance Indicators Pertaining to the Patient Flow

This article has developed specifications for a new model-driven decision support system (DSS) that aids the key stakeholders of public hospitals in estimating and tracking a set of crucial performance indicators pertaining to the patients flow. The developed specifications have considered several requirements for ensuring an effective system, including tracking the performance indicator on the level of the entire patients flow system, paying attention to the dynamic change of the values of the indicator’s parameters, and considering the heterogeneity of the patients. According to these requirements, the major components of the proposed system, which include a comprehensive object-based queuing model and an object-oriented database, have been specified. In addition to these components, the system comprises the equations that produce the required predictions. From the system output perspective, these predictions act as a foundation for evaluating the performance indicators as well as developing policies for managing the patients flow in the public hospitals.

Using Queue Theory and Load-Leveling Principles to Identify a Simple Metric for Resource Planning in a Pediatric Emergency Department

Increased waiting time in pediatric emergency departments is a well-recognized and complex problem in a resource-limited US health care system. Efforts to reduce emergency department wait times include modeling arrival rates, acuity, process flow, and human resource requirements. The aim of this study was to investigate queue theory and load-leveling principles to model arrival rates and to identify a simple metric for assisting with determination of optimal physical space and human resource requirements. We discovered that pediatric emergency department arrival rates vary based on time of day, day of the week, and month of the year in a predictable pattern and that the hourly change in pediatric emergency department waiting room census may be useful as a simple metric to identify target times for shifting resources to better match supply and demand at no additional cost.

Composite Monte Carlo decision making under high uncertainty of novel coronavirus epidemic using hybridized deep learning and fuzzy rule induction

In the advent of the novel coronavirus epidemic since December 2019, governments and authorities have been struggling to make critical decisions under high uncertainty at their best efforts. In computer science, this represents a typical problem of machine learning over incomplete or limited data in early epidemic Composite Monte-Carlo (CMC) simulation is a forecasting method which extrapolates available data which are broken down from multiple correlated/casual micro-data sources into many possible future outcomes by drawing random samples from some probability distributions. For instance, the overall trend and propagation of the infested cases in China are influenced by the temporal–spatial data of the nearby cities around the Wuhan city (where the virus is originated from), in terms of the population density, travel mobility, medical resources such as hospital beds and the timeliness of quarantine control in each city etc. Hence a CMC is reliable only up to the closeness of the underlying statistical distribution of a CMC, that is supposed to represent the behaviour of the future events, and the correctness of the composite data relationships. In this paper, a case study of using CMC that is enhanced by deep learning network and fuzzy rule induction for gaining better stochastic insights about the epidemic development is experimented. Instead of applying simplistic and uniform assumptions for a MC which is a common practice, a deep learning-based CMC is used in conjunction of fuzzy rule induction techniques. As a result, decision makers are benefited from a better fitted MC outputs complemented by min–max rules that foretell about the extreme ranges of future possibilities with respect to the epidemic.

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Composite Monte-Carlo (CMC) simulation is a forecasting method.

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A case study of using CMC through deep learning network is developed.

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Decision makers are benefited from a better fitted Monte Carlo outputs.

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Novel Coronavirus Epidemic is studied.

Impact of the implementation of a fast-track on emergency department length of stay and quality of care indicators in the Champagne-Ardenne region: a before-after study

OBJECTIVES

We aimed to evaluate the effect of the implementation of a fast-track on emergency department (ED) length of stay (LOS) and quality of care indicators.

DESIGN

Adjusted before-after analysis.

SETTING

A large hospital in the Champagne-Ardenne region, France.

PARTICIPANTS

Patients admitted to the ED between 13 January 2015 and 13 January 2017.

INTERVENTION

Implementation of a fast-track for patients with small injuries or benign medical conditions (13 January 2016).

PRIMARY AND SECONDARY OUTCOME MEASURES

Proportion of patients with LOS ≥4 hours and proportion of access block situations (when patients cannot access an appropriate hospital bed within 8 hours). 7-day readmissions and 30-day readmissions.

RESULTS

The ED of the intervention hospital registered 53 768 stays in 2016 and 57 965 in 2017 (+7.8%). In the intervention hospital, the median LOS was 215 min before the intervention and 186 min after the intervention. The exponentiated before-after estimator for ED LOS ≥4 hours was 0.79; 95% CI 0.77 to 0.81. The exponentiated before-after estimator for access block was 1.19; 95% CI 1.13 to 1.25. There was an increase in the proportion of 30 day readmissions in the intervention hospital (from 11.4% to 12.3%). After the intervention, the proportion of patients leaving without being seen by a physician decreased from 10.0% to 5.4%.

CONCLUSIONS

The implementation of a fast-track was associated with a decrease in stays lasting ≥4 hours without a decrease in access block. Further studies are needed to evaluate the causes of variability in ED LOS and their connections to quality of care indicators.