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  • Writer's pictureEMVOKE Technologies

Healthcare Management: Enhance Patient Experience by predicting patient in-flow and queue time.

The worldwide health care sector is hampered by delays. We are accustomed to making an appointment with a doctor or scheduling a procedure, then waiting again once we go to the doctor's office before being seen. Patients waiting for beds in hospital halls are common, and there are frequently delays with surgery or diagnostic procedures.

More than 50% of patients who are admitted to hospitals enter through the emergency rooms (ER), which results in extreme patient overcrowding in most hospitals.

The emergency room is a crucial component of hospitals, and as a result, most divisions need a lot of resources because of the long patient lines.

In a place like healthcare, waiting in lines can increase the risk factor since it can not only cost healthcare providers money but also be uncomfortable for patients. The patient's life or health problems could also be affected by it.

Waiting has several other negative effects also such as low service quality, delayed treatments, financial costs, and more.

According to the government, the doctor-to-patient ratio in developing countries like India is 1.34:1000 patients, and for specialties like dermatology, it is closer to 1:8000. This increases the number of OPD patients who must be seen quickly.

In order to go to an emergency room or intensive care unit when needed, doctors in hospital OPDs occasionally have to pause the line. This adds to the queue's problems.

The Time Spent:

The majority of patients (164, 78.1%) wait less than one hour to see a doctor and spent no more than two hours in line before being treated.

The majority of patients (144, 68.5%) weren't satisfied with how long they had to wait in line before being seen by a doctor.

The following were helpful recommendations made by the patients to reduce the amount of time spent waiting in line to see a doctor at the clinic: hire more doctors ( 21.9 %); require doctors to arrive at work on time (11.9%); and strictly adhere to the first-come, first-served policy (15.2 %).

Managing the patient wait list and calculating wait times is a highly challenging task.

The type of patient, symptoms, findings, disease, examination, report, and investigations, the frequency of patient visits, and patient counseling all affect the queue time.

Thereby, patient queue management and wait time prediction is a difficult and complicated responsibility because each patient may require different phases/operations during treatment, such as a check-up, various tests, sugar level or blood test, X-rays, or a Computerized Tomography (CT) scan, and minor surgeries.

Each treatment task may have different time requirements for each patient, making time prediction and recommendation extremely difficult. According to his health, a patient is typically asked to undergo examinations, inspections, or tests (referred to as tasks). For each patient, more than one activity might be necessary for this situation.

While some of the jobs can be completed independently, others may need to wait for the conclusion of dependent tasks. The majority of patients must wait in lines for unpredictably long times while they wait their turn to complete each treatment task.

Patients who waited in line for less time (less than one hour) were more satisfied than those who waited in line for longer. Therefore Queuing system in the health care system is very much desirable.

The clinic uses the multiple single channel style of queuing, and priority service is the service discipline.

For decades, queuing systems have been studied using the classical mathematical method known as queuing theory (QT). Applying queuing theory is a call to action for improving patient flow throughout our complicated industry now more than ever.

Queuing theory addresses delays brought on by a mismatch between demand for a service and the available capacity to provide it. A queuing model's goal is to strike a compromise between customer service (shorter wait times) and resource constraints (number of servers).

Patient queuing models can assist in predicting responses to issues about patient flow, including:

  • How much time would the typical patient be needed to wait?

  • How long does a typical visit last?

  • How likely is it that a patient will have to wait more than 20 minutes?

  • How much time does a typical patient spend with the provider?

  • How many employees are required to see every patient within ten minutes?

  • Will a different triage procedure result in better patient flow?

  • How common is it for a hospital to send patients elsewhere?

The process flow for the emergency department is depicted in Fig. 1, along with the related problems it deals with. The diagram illustrates how patients move through the healthcare system and highlights how interdependent departments must coordinate.

Patient Flow detection & prediction:

Hospitals and clinicians must strike a balance between properly treating each patient's illness and dispersing healthcare resources to patient populations over time.

Patient flow, a typical metric of patient safety, satisfaction, and access, is linked to patient capacity and resource management in hospitals.

An ideal patient flow encourages effective care, less waiting, little exposure to hospital dangers, and effective resource usage (e.g., of beds, clinical staff, and medical equipment).

Access to specialized inpatient services is also influenced by the patient flow.

Hospitals are under enormous economic pressure to provide effective and accessible treatment. The cost of healthcare as a proportion of GDP (17.9%) has been rising more quickly than expected, and between 30 and 40 percent of these costs have been linked to "overuse, under-use, abuse, duplication, system failures, excessive repetition, poor communication, and inefficiency."

These elements hinder patient flow, lengthen hospital stays, and raise the price of care per patient.

Patient flow, and consequently bed and capacity management, is a typical area of focus for operations management techniques used in the healthcare industry.

Discrete-event simulation, optimization, and Lean Six Sigma methods have been successfully used in a variety of settings to improve patient flow by redesigning care delivery processes or more efficiently matching staff and other resources (e.g., operating rooms, medical equipment) to demand.

These patient flow assessments are data-driven and help to inform long-term operational decisions. These studies' outcomes include improved patient and staff scheduling strategies, new bed management policies, and reduced variability in the care process.

1. Real-time demand capacity management:

Alternately, a more recent development in patient flow management concentrates on immediate operational choices. When real-time demand capacity management (RTDC), a new technique created by the Institute for Healthcare Improvement, was pilot tested in hospitals, the results were encouraging but inconsistent.

The RTDC method entails four steps:

  • Capacity prediction;

  • Demand prediction;

  • Plan development; and

  • Plan evaluation.

The morning clinician huddle is the focal point of the RTDC process, where it is decided which and how many patients will be discharged that day.

The RTDC method has shown that the strategy may lessen important indications of patient flow across hospitals after an initial learning phase. These metrics include the amount of time spent boarding in the ED, the number of patients who left without being seen, and overnight holds in the patient care unit.

2. Forecasting models

These models have been used to forecast hospital occupancy, patient arrivals and departures, and other operational variables that are specific to each unit. These models were created by combining different auto-regressive moving average techniques, exponential smoothing, Poisson regression, neural networks, and discrete event simulation techniques.

In more recent investigations, patient LOS was predicted using logistic regression and survival analysis techniques. Clinical staff can effectively schedule upcoming appointments or admissions to prevent backlogs or denials by accurately predicting patients' LOS.

3. Machine Learning

Machine Learning Tree-based algorithms have been used in the healthcare industry to

  • Forecast a continuous-valued result or

  • Categorize patients into one or more clinical groupings.

To forecast the range of motion for orthopedic patients, expenses, and use, for instance, one may use regression trees or linear regression[1].

It has been used to distinguish between benign and malignant tumours, identify patients most likely to benefit from screening treatments, identify high-risk individuals, and forecast particular clinical outcomes. An example of the latter is generally logistic regression or classification trees.

More recent applications of more sophisticated machine learning techniques, including bagging, boosting, random forests, and support vector machines, have been made to healthcare issues such as categorizing patients with heart failure and estimating healthcare expenses.

Case Study on patient flow and prediction data:

The investigation was carried out in a single, 36-bed medical unit at a significant academic medical facility that treats urban residents.

Internal medicine doctors without any responsibility for teaching work in the unit. Over a 34-month study period from January 1, 2011, to November 1, 2013, 9636 patient visits totaling patient flow information (i.e., admission and discharge periods), demographics, and fundamental admission diagnosis data were gathered.

The data were kept for 8852 patient visits after eliminating inaccurate and partial records, converting these visits to N = 20243 individual patient days. Table 1 summarizes these data.

The prediction of individual patient discharges was done through systematic experimentation using popular supervised machine-learning techniques. These techniques comprised classification and regression trees, logistic regression (the so-called reference approach), and tree-based ensemble learning techniques. For the predictive measure, model thresholds and parameters were adjusted for optimum performance.

Then, using repeated data partitioning into groups with comparable properties and results, tree-based algorithms are employed to forecast patient discharge outcomes.

Fig. 2 gives an illustration of how the findings could be communicated to physicians by visualizing the classification tree for end-of-day discharge predictions.

Fig.2: Classification tree for end-of-day discharge predictions

Conclusions for the case study:

In comparison to physicians, the model predicted discharges with better sensitivity and lower specificity, and the two approaches were comparable in terms of overall accuracy. However, for several near-future and overall prediction measures, the machine learning model did outperform the clinicians.

Therefore, there is a strong possibility that these models will automate and speed up the RTDC prediction process, obviating the requirement for daily clinician huddles or supporting more precise clinician forecasts.

Basic Queuing Concepts and Types of Queues:

A queue is distinguished by its arrival and service processes, the number of servers, and the service discipline. The arrival process is defined by a probability distribution with an associated arrival rate, which is typically the mean number of patients arriving during a time unit (e.g., minutes, hours, or days)[2].

A queuing network commonly occurs when patients share and use multiple resources. Consider a patient who visits the Orthopedic outpatient clinic and then requires an X-ray at Radiology; or a surgical patient who is operated on in the OR and then cared for in the Intensive Care Unit (ICU), and finally in a nursing ward[3].

Fig.3: presents a simple queue process.

The Poisson Process:

The Poisson process, in which patient arrival times are independent and exponentially distributed, is a popular choice for the probabilistic arrival process.

The Poisson process is prevalent in real-world processes and has several fascinating and extremely helpful qualities for analysis.

The arrivals in any given period follow a Poisson distribution. If N(t) is the number of arrivals over a while of t and N(t) has a Poisson distribution.

Probability {N(t) = n} = e^' (Xif/n!

where ʎ is referred to as the rate and represents the expected number of arrivals per unit time.

The M/M/S model:

The M/M/s or Erlang delay model is the queuing model that is most frequently employed. In this paradigm, there is a single line that feeds onto identical servers and has an endless waiting area.

Customers come in a Poisson process at a constant rate, whereas the length of the service is distributed according to an exponential distribution. (These two presumptions are frequently referred to be Markovian, which is why the model's notation uses two "M's."

Fig.4: Transition rate in M/M/S queue

If the system comprises patients at any one time and is in statistical equilibrium, with probability P_n:

P_n = limit→∞ P(N(t) = n)

The probability P_n also shows the percentage of time when there are n patients in the system. The overall probability can be compared to a volume of fluid that is dispersed among the Markov chain's states and flows from one state to the next according to the transition rates.

The M/G/1 and G/G/s models :

The M/M/s may drastically underestimate or overstate actual delays if the CV differs much from one.

In that case, the following formula for the so-called M/G/1 system can be used to determine the average latency for any service distribution even if there is only one server and the arrival process is Poisson:

W_q = [ʎ_p/(l-p)][(l + 〖CV〗^2 (S))/2]

Here 〖CV〗^2 (S) is the square of the coefficient of variation of the service time. The queue load is classified as the mean utilization rate per server, which is the average amount of tasks that arrive per time unit divided by the average amount of tasks that the queue can manage per time unit.

Fig.5: The relationship between load and mean waiting time for the M/M/1 queue with Poisson arrivals and exponential service times

For 〖CV〗^2 (S)=1, the relation is visually depicted in Fig. 5. We can observe that when the load grows, the mean waiting time grows as well. When the load is low, the mean waiting time is not significantly affected by a slight increase in the load. The mean waiting time, however, is greatly impacted by even a slight increase when the load is high.

Fig.6: Transition rate in M/M/1 queue

AI and Machine learning in Queuing model for Healthcare:

The queuing theory uses mathematical analysis to try to understand the waiting lines.

Queue managers use queuing theory to balance a queuing system's service to customers by keeping the queues short and so reducing waiting times, as well as the financial maintenance of the system. A queuing model can be built to anticipate the wait time for any client and the queue size at any given moment.

Artificial intelligence is widely used to estimate flows and loads through/on various types of systems as well as predictions on various forms of time series. Machine learning, the study of developing software programs that learn and adapt when presented with new data, is one of the main sub-fields of artificial intelligence.

The algorithms base their induction, which improves efficiency, on data from things like observations or statistics.

Queuing issues can be solved using machine learning approaches. When compared to the imprecise estimations that are generally given to patients, a regression model was able to anticipate the total waiting time for daily radiation treatment appointments more accurately.

Fig.7: Diagram of a typical machine learning algorithm

We refer to separate OPD Clinic Queues and Inpatient Emergency - IPD Queues; both approaches have differences. We offer answers for both.

Recommendations for OPD Clinic Queue:

• If the doctor so decides, track their availability with caution.

• Send a reminder or notification from before.

• The ability to pause the line for appointments with doctors average time management.

Predict inflow based on :

  • Patients in Line,

  • Appointments Scheduled for Today,

  • Forecasting the Inflow of Walk-In Patients.

  • Medical history and specialization.

Computer systems are now able to learn from huge, possibly complicated information and provide real-time prediction functions thanks to technological advancements like machine learning. Machine learning's core purpose is to make predictions about the future using knowledge gained from the past.

The machine learning algorithm may be guided to complete its mission by the definition of an initial feature set based on the practical experience of healthcare expert.

Other easily accessible information, such patient demographics and the day and time of the week, were employed as features. The intended list of features used for the investigation is shown in Table 1.

Table1: List of features extracted from the input sample

Testing and comparison are done on four machine learning regression models.

  • Support vector machines,

  • decision trees,

  • random forests, and

  • linear regression.

Eighty percent of the entire retrospective data-set was randomly sampled to create the training set, and the remaining twenty percent was used for testing.

A comparison of the applied regression models, together with performance indicators and the kind of preprocessing utilized, are shown in Table 2.

By measuring the mean and median absolute errors of the forecast from the actual value, as well as the standard deviation of these errors, the accuracy of the regression models was compared.

Table2: Evaluation of each machine learning regression model's performance


Decisions on how and when to allocate staff, equipment, beds, and other resources in healthcare facilities to minimize patient delays are frequently more difficult than in other service industries due to cost constraints on the one hand and the potentially serious adverse consequences of delays on the other. As a result, it is critical that these decisions be as well-informed as possible, and that they rely on the best methodologies available to gain insights into the impact of various alternatives.

Queuing analysis should be employed frequently in the healthcare industry since it is one of the most useful and efficient techniques for comprehending and assisting decision-making in managing vital resources.

The usage of artificial neural networks taught by a supervised learning algorithm might be used to forecast patient flow, and when integrated with queuing theory, could be used to optimize staff scheduling.

EMVOKE Health-stack can help Hospital SaaS providers, Hospitals and Clinicians implement AI-based Predictive Queuing for enhanced Patient Experience and for better management of Doctor time.


[2] Application of queuing theory to patient satisfaction at a tertiary hospital in Nigeria,Nkeiruka Ameh, B. Sabo, M. O. Oyefabi Niger Med J. 2013 Jan-Feb; 54(1): 64–67. DOI: 10.4103/0300-1652.108902

[3] Preater, J., (2001), A bibliography of queues in health and medicine, Mathematics Department, Keele University, 2001.


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