Managing Emergency Units Applying Queueing Theory

Managing Emergency Units Applying Queueing Theory

Salvador Hernández-González (Instituto Tecnologico de Celaya, Mexico), Manuel Dario Hernández-Ripalda (Instituto Tecnologico de Celaya, Mexico), Anakaren González-Pérez (Instituto Tecnologico de Celaya, Mexico), Moises Tapia-Esquivias (Instituto Tecnologico de Celaya, Mexico) and Alicia Luna-González (Instituto Tecnologico de Celaya, Mexico)
DOI: 10.4018/978-1-5225-0130-5.ch022


Today managers of health systems must manage the resources at their disposal to ensure that service quality is adequate, this leads at the same time making decisions to ensure that these resources are managed efficiently and effectively. The decision process in healthcare systems is not trivial given the complexity of these systems. The application of tools (like queueing theory) for decision making in hospital systems is an area of opportunity because of the increasing financial pressure and the growing demand for care. This document shows how queueing theory can be applied for analyzing the performance of an Emergency Unit under different capacity scenarios. The analysis shows that increasing the number of servers required to maintain constant congestion(emphasis on efficiency)is more expensive than adding servers to maintain constant the probability that a patient has to wait (emphasis on quality and efficiency). The paper ends with recommendations for future research.
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Administration of Health Systems and Hospitals

Hospital systems administrators are responsible for managing resources at their disposal, in order to provide quality service to patients and beneficiaries.

Hospital systems were used to operate without major limitations regarding the available resources, since it was essential to preserve the integrity of the patient, also administration was supported to a greater extent by trial and error, therefore, the application of tools from different areas, as Operations Research have been (at least until recently) ignored; but today health institutions, especially government institutions suffer from increasing financial pressure from governments, which require that assigned resources are managed effectively and efficiently.

While this applies to all hospitals in the world, it is in the countries known as emerging economies such as Mexico, where the effects of lack of tools to support the decision process have a greater impact. As others, Health systems are not easy to analyze and problems are challenging.

For example: Mexico is among the few OECD countries that have not yet achieved universal or near universal coverage of health insurance. Also, the public share of health care financing in México has increased to 50% in 2012, but it is one of the lowest across the OECD members (the average is 72%) (OECD 2005, OECD 2014), in other words, around half of all health spending is paid by Mexican patients.

Expenditure cuts to the health systems are common and result in the zero generation of vacancies for new doctors and nurses, shortages of medicines, materials and equipment; however it continues increasing demand service. According to OECD statistics, in Mexico the number of doctors per capita raised in the past years moving from 1.6 per 1000 population in 2002 to 2.2 per 1000 population in 2012, which it is just above Korea (2.1), Chile(1.7) and Turkey(1.7). The 34 members of the OECD average 3.2 (OECD, 2014).

It should be noted that one of the priorities of governments should be to ensure greater coverage of health services, ensuring that the workforce (doctors, nurses) have the necessary skills and resources to carry out their tasks.

The question arises about what managers should do before making a decision. According to Litvak, Long, Arroye and Jarillo (2000) the following question is proposed: How much can be cut in spending of a health system without affecting the quality of service?

In Health systems timely access has been identified as one of the key elements of healthcare quality (Green 2005). What kind of tools can be applied to measure the time a patient spends waiting in a queue to receive attention? How many doctors are needed to guarantee a reasonable waiting time and generate the perception of a good quality in the service? How much a “good” policy cost?

This chapter shows a set of relationships derived from queuing theory which are (among many others) very useful for decision-making and enable an administrator to evaluate different decisions and also their impact on the quality of service provided to patients and so to answer questions as the previous paragraph. We present an application example of the emergency system of a public hospital in Mexico where it is necessary to calculate the number of doctors required to satisfy the demand of service and ensuring the quality of service, the costs of different alternatives and the robustness to face scenarios of increased demand.

Key Terms in this Chapter

Customer: Entity requiring or requesting service (person, piece, part).

Cycle Time: Time spent by a customer from entering the system until it is removed.

Queueing Theory: It is the study of the phenomenon of waiting to be served, trying to predict the time in the system as well as the average number of customers.

Waiting Cost: The cost incurred by each client to expect formed to be addressed. In the case of hospital systems this cost is infinite.

Triage: A classification system used by doctors of Emergency Units for the selection and classification of patients based on the priorities of care, favoring the possibility of survival, according to the therapeutic needs and available resources.

Patient Flow: Movement of customers in a hospital through each stage of care treatment.

Hospital: A facility where sick customers are cared for to provide diagnosis and treatment.

Healthcare System Management: Set of techniques and tools applied to the effective and efficient management of resources in health systems, hospital systems and in general all those dedicated to the diagnosis, treatment and cure of diseases of persons.

Service Cost: Resource cost per patient treated.

Work in Process: Number of customers waiting to be served.

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