A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management

Dai, J. G.; Shi, Pengyi

doi:10.1287/opre.2016.1566

Cited by 48 publications

(35 citation statements)

References 39 publications

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“…Thus, it is sufficient to focus on t ∈ [0, 1). Readers are referred to section 3 of Dai and Shi (2017) for the detailed formula of calculating the stationary distribution of X ( t ), as well as various steady‐state, time‐dependent performance, such as the mean queue length

{double-struckE}_{\infty} false[Q (t) false] = {double-struckE}_{\infty} {[X false(t false) - N]}^{+}

, mean waiting time

{double-struckE}_{\infty} false[W (t) false]

, and tail of waiting time

{double-struckP}_{\infty} false(W (t) > 6 hours false)

, t ∈ [0, 1).…”

Section: Analytical Methods For the Two Service Time Modelsmentioning

confidence: 99%

“…The single‐pool system needs the following input in addition to the service time component: bed capacity N , and rate function λ ( t ) for the non‐homogeneous Poisson arrival process. Based on the hospital data provided in Dai and Shi (2017), we test two experiment settings in section 2.2.2: (i) Assuming all hospital beds are pooled, we have N = 530, and the hourly pattern for λ ( t ) as illustrated in Figure 2a. The daily arrival rate, defined as

Λ = \int_{0}^{1} λ false(t false) d t,

equals 90.95 patients per day.…”

Section: Service Time Modelsmentioning

confidence: 99%

“…When L ∼ geo( μ ) takes the geometric distribution, while

S \sim \exp (μ_{S})

takes the exponential distribution, the two service time models relate to each other through the well known property on the ceiling of exponential random variable, that is,

⌈ S ⌉ \sim geo (1 - \exp false(- μ_{S} false)) .

(We use ∼ to denote “having the same distribution with.”) By noting this relationship, the two service time models essentially become equivalent on each sample path by letting

μ = 1 - \exp (- μ_{S})

. Moreover, the stability condition provided in Dai and Shi (2017) and the stability condition provided in Dong and Perry (2019) become equivalent. That is, when d =0,

β = 1 - \exp false(- μ_{S} false) = μ .

…”

Section: Service Time Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management

Dai

Shi

2021

Production and Operations Management

Self Cite

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I npatient flow management plays a critical role in care delivery, patient outcomes, and hospital operational and financial costs. Modeling and performance analysis of inpatient flow present unique features and challenges that differ from operations in other service industries. In this study, we review recent modeling and analytical advances in the setting of inpatient flow management, with a particular focus on service time models motivated from the observations of inpatient discharges. We first compare two new service time models developed to capture the time-of-day inpatient flow dynamics, and reveal interesting connections between the two models. We then review analytical methods developed to analyze systems with the new service time models. Based on one method, which is amenable to a one-dimensional exact analysis under certain conditions, we further introduce its approximations that have explicit analytical forms and enable efficient computations in large systems. In particular, we showcase how to leverage a powerful tool, Stein's method framework, in the hospital setting for steady-state approximations and characterizing error bounds. We conclude this study by a literature review on other important aspects in inpatient flow management and propose future research directions, from both the modeling and analytical perspectives.

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{double-struckE}_{\infty} false[Q (t) false] = {double-struckE}_{\infty} {[X false(t false) - N]}^{+}

, mean waiting time

{double-struckE}_{\infty} false[W (t) false]

, and tail of waiting time

{double-struckP}_{\infty} false(W (t) > 6 hours false)

, t ∈ [0, 1).…”

Section: Analytical Methods For the Two Service Time Modelsmentioning

confidence: 99%

Λ = \int_{0}^{1} λ false(t false) d t,

equals 90.95 patients per day.…”

Section: Service Time Modelsmentioning

confidence: 99%

“…When L ∼ geo( μ ) takes the geometric distribution, while

S \sim \exp (μ_{S})

takes the exponential distribution, the two service time models relate to each other through the well known property on the ceiling of exponential random variable, that is,

⌈ S ⌉ \sim geo (1 - \exp false(- μ_{S} false)) .

(We use ∼ to denote “having the same distribution with.”) By noting this relationship, the two service time models essentially become equivalent on each sample path by letting

μ = 1 - \exp (- μ_{S})

. Moreover, the stability condition provided in Dai and Shi (2017) and the stability condition provided in Dong and Perry (2019) become equivalent. That is, when d =0,

β = 1 - \exp false(- μ_{S} false) = μ .

…”

Section: Service Time Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management

Dai

Shi

2021

Production and Operations Management

Self Cite

View full text Add to dashboard Cite

show abstract

“…Managing LOS in heart failure is an area that operations research and analytical tools can substantially help address. Truong (2018) surveys the healthcare operations management literature on inpatient management that has a clear prescriptive focus and relies on queueing theoretical tools to develop inpatient ward policies (eg, J. G. Dai & Shi, 2017) and discharge planning tools (eg, Chan, Dong, & Green, 2017) that affect a patient's LOS. The medical literature, on the other hand, focuses on factors driving the LOS and developing predictive‐analytics tools (Whellan et al, 2011; Tashtish, Al‐Kindi, Oliveira, & Robinson, 2017).…”

Section: Heart Failurementioning

confidence: 99%

Heart analytics: Analytical modeling of cardiovascular care

Dai

Gleason

Hwang

et al. 2019

Naval Research Logistics

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Cardiovascular diseases (CVDs) are the leading cause of death and disability both in the United States and worldwide. Despite high morbidity, mortality, and cost in the United States and global healthcare systems, cardiovascular care has been understudied in the healthcare operations management literature. In this paper, we identify research opportunities for healthcare operations management scholars to aid in improving cardiovascular care. We focus on three burdensome conditions, including (1) coronary artery disease, (2) stroke, and (3) heart failure, which, collectively, lead to the vast majority of CVD‐caused mortality and disability. For each condition, we characterize a typical patient's journey in receiving cardiovascular care, elucidating key challenges in improving care and outlining research questions for healthcare operations management scholars. We close with a reference to new research opportunities that emerge as artificial intelligence is likely to transform much of cardiovascular care.

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“…Accurate estimation of flow rates can also help predicting other ED workflow variables, such as time-to-treatment and length-of-stay [14] when the ED is modeled as a queueing system. In [15], flow variables that mimic arrival and treatment rates are combined with machine learning to estimate time-to-treatment for each patient, and in [16], [17], a queueing theoretic version of that approach is used to estimate the length-of-stay for each patient. Approaches that model the ED as a queueing system are hindered by unexplained queue pre-emption and delays (see Section III).…”

Section: Introductionmentioning

confidence: 99%

PatientFlowNet: A Deep Learning Approach to Patient Flow Prediction in Emergency Departments

Sharafat

Bayati

2021

IEEE Access

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Emergency Department (ED) crowding is a major public health challenge since it can seriously impact patient outcomes; and accurate prediction of patient flow in EDs is essential for improving operational efficiency and quality of care. We present a deep learning framework to predict patient flow rates in EDs, namely the rates of arrival, treatment, and discharge for patients across all triage levels. Our model detects short-term and long-term temporal dependencies within the time-series data of a given patientflow variable, as well as dependencies between time-series data of different patient-flow variables. We implement this framework as a convolutional neural network, which we call PatientFlowNet. Our proposed model learns simultaneously from multiple flow variables over a long temporal window and predicts future values of arrival, treatment, and discharge rates in the ED. We benchmark our model against state-of-the-art methods on data from EDs in three different hospitals. Results show that PatientFlowNet achieves superior prediction accuracy, compared to the baseline methods, and yields a mean absolute error that is 4.8% lower than the leading baseline. Furthermore, we provide a visual and interpretable representation of the learned dependencies by our model, between patient-flow variables in EDs. INDEX TERMS Health information management, machine learning, neural networks, public healthcare, supervised learning.

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A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management

Cited by 48 publications

References 39 publications

Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management

Recent Modeling and Analytical Advances in Hospital Inpatient Flow Management

Heart analytics: Analytical modeling of cardiovascular care

PatientFlowNet: A Deep Learning Approach to Patient Flow Prediction in Emergency Departments

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