Reduction of Boarding Times to the Emergency Department

Emergency hospital services (ED) was the main hospital entrance door and so was the almost obligatory passage for patients before admission in most health units. The practice of blocking admitted patients (patients IP) on stretchers in the corridors of the hospital emergency services for hours or days, called "boarding" causes emergency space and can be harmful to patients. Boarding increases patient morbidity, length of hospital stay, and mortality. In this article, we make the modeling of boarding patients in the emergency department to minimize overcrowding in emergency departments, using a network of queues open to the MMC. The results of this paper help the hospital administration to test alternative policies to improve overall performance.


1.INTRODUCTION:
The hospital emergency departments (ED) are an essential element in the movement of patients in a hospital.Emergency services typically have large volumes of patients, working under high use service many types of patients, and patients go out of most other areas of the hospital.Although the majority of patients in the emergency department returned to the house, about 20% of ED patients are referred to an IP device (IP patient) such as intensive care units, operating room, obstetric units.
One patient remained IP (board) to the hospital emergency department (ED) it is admitted to an IP unit and has no bed available.
The main problems caused by boarding patients in the emergency department ED -Decrease the ability of ED service using emergency rooms with patients boarded.
-Increased waiting time ED patients, an increase in patients leaving without treatment because of the long waiting time The purpose of this article is to provide a useful aid to decision makers for the service, and modeling boarding patients in the emergency department.
The article is structured as follows.
In section 2, the analysis of the state of the art.
In section 3, the modeling problem is presented.
In section 4, hospital estimation of ed boarding.

1-STATE OF THE ART:
Given its complexity, the emergency department has been the subject of numerous studies dealing with issues related to the modeling, simulation and optimization of patient flow.In this sense, [Chaussalet et al, 2006] aims to model the flow of patients in a health care system with an application in a geriatric ward in the UK, to provide a useful decision aid for the controller service.They use a closed network of queues with the hypothesis of a system always full.This means that the system operates at maximum capacity, the waiting list admissions to hospital is never empty, and in each phase output is immediately replaced by a new admission in the first phase.Using data from a Department of Geriatrics in the United Kingdom which contains three phases (acute care, rehabilitation and long-stay care).
Gorunescu et al (2002) use a model queue M / PH / c / N to show how the use of waiting rooms can improve performance while controlling costs.Using statistical data and the theory of queues, they show how changes in three performance criteria (length of stay, admission rates, allocation of beds) influence bed occupancy, release into the geriatric department.
Against this backdrop, Koizumi et al (2005) extend the existing studies in the literature on networks of queues with blocking to analyze congestion in a psychiatric hospital in Philadelphia.Mathematical results and the simulation results are presented and compared.First, they use a model without blocking.Then they analyze this model with blocking by introducing the concept of "effective time of service", which contains two types of service time, called "processing time" and "blocking time".Model queues focuses on the phenomenon of blocking three psychiatric departments and the allocation of resources.The simulation is then used to analyze the behavior of the system and test the robustness of the proposed mathematical model.If the simplified mathematical model is useful for analyzing long-term performance, the simulation models are essential for the analysis of short-term performance.
Bruin et al (2007) examine the congestion patient flow in the department of cardiac emergencies.They want to determine the optimal allocation of beds for several levels of service given a maximum number of denied admission.Another objective is to show the relationship between natural variation in arrival, length of stay and occupancy rates.For the data they used, they verified that all admission rates and service time always follow the Poisson and exponential distribution and they study each department individually as a / M queue M / c / c.In this article, we make the modeling of boarding patients in the emergency department by using a network of queues open to the MMC.
Modeling the boarding of patients in emergency departments can be quite difficult because of the complex network of IP devices and the necessary theoretical models queues input estimates.

1-MODELING Network queues
A network of queues [Gelenbe and Pujolle, 1998] is a set of stations queue consisting of a queue, where the entities are waiting for a service and a server on which the entities enjoy a service.Network theory of queues allows the calculation of several performance criteria, including the average waiting time in the queue or in the system (in our case, this is the queue of patients), the average number of patients waiting to receive a service.D e c e m b e r 3 1 , 2 0 1 4 This section presents a model of the theory of queues and estimation methodology to quantify ED boarding time.This method considers the Emergency Department as two multi-server Markov queues in series.The system studied is clearly stochastic, by the arrival of unpredictable emergencies and random times of the waiting time.This naturally refers to the theory of queues.Indeed, assuming a Poisson arrival process emergencies.Variables with the "Hospital data" type are variables that are directly estimated from hospital data.Variables "Fit model" type variables are fixed with queues based on statistical estimates described below.Variables "estimation model" type are variables that are estimated by the queue after statistical adjustment.
The model assumes that the system is in a stable state.To mount the service level, we use the method of moments of statistical estimation.The method of moments is a statistical estimate approximates the distribution parameters estimates based on the sample moments in the data.The performance is evaluated by the hospital boarding probability, namely the probability that the patient refused.
Too high a probability boarding indicates the need to increase the capacity of health units (add additional hours for surgeons, add beds, increase the time of use rooms surgeries).
Calculate the optimal value sought to be built so that it minimizes the value K: the rate increased resources in IP care units

CONCLUSION
We presented a method to estimate the time of boarding patients in the ED through the use of networks of queues.The model considers the emergency and standby ip as two markov queues in series.statistical estimation is used the method of moments where variables used in this model are estimated so that the resulting estimates of waiting and boarding time is roughly equal to estimates of hospital data.
This formulation was motivated by research that finds ED boarding is problematic in many hospitals.The case study of the hospital found that small percentage increase in the capacity of health units produce significant reductions in ED boarding and waiting.

Figure 1 :
Figure 1: The ED and IP displayed as two queues in series.

utilization ratio Equation 1 :Equation 2 :Equation 3 :
Expected Value of waiting time in the unit ED.Represents the rate of ED service.In practice, the service time of ED equals the time the patient is treated with more urgency the time the patient is stuck in an emergency.Therefore, the service rate of ED should can be written as a function of time of treatment provided in the emergency department without waiting .utilization ratio.Expected Value of boarding time for patients admitted to the unit IP.

4 :
Estimating the optimal rates

Equation 3 and 4 :Table 2
Figure a and b show the percent reduction of loading and nominal reduction and percent of ED expected wait time.