There are several approaches related to health care management and management indicators based on processes in hospital institutions; they can be summarized in two main visions: clinical (clinical management) and administrative (hospital processes management)¹.

Hospital facilities play a predominant role within the National Health System. They are characterized by providing specialized medical care and preventive, curative and rehabilitative nursing care on an uninterrupted basis to all their patients, in addition to providing inpatient, outpatient and emergency services.

Healthcare has evolved from the traditional view towards a more active participation of the patient in the care process. This new approach enhances the participation of patients and accompanying persons in the management, as well as in the development of health services². In addition, the need is recognized that health services, like any other type of entity, must be properly planned, organized, directed and controlled^3,4.

Thus, it is recognized how improvements to hospital management guarantee that standardization results in the optimization of care, product of the transformation of inputs into output as in itself is the welfare of people¹, through an integrated, systematic and efficient management, which offers sustained functionality, supported by scientific and technological advances, according to the planned goals and purposes⁵.

In hospitals there is evidence of movement of patients through a variety of departments, facilities and physical locations at any time, to be attended by different specialists and technicians; this movement is recognized in literature as patient flow. Dawoodbhoy et al⁶. define it as the ability of healthcare systems to manage patients care demands efficiently by reducing waiting times between treatment stages and average length of stay, while maintaining service levels and patient satisfaction at all times.

Organizing patient flows represents a major challenge for administrators, as medical activity has inherently high variability, which makes it very complex. Thus, identifying the origins of the flows is emerging as an element of great importance that supports decision making. Duarte Forero and Camacho Oliveros⁷ state that they are generated through the outpatient department (outpatient consultation), emergencies (on-call department), or referrals from other health institution.

Improving patient flow along the process is a long-term work that requires synchronization between all the processes involved. A basic step for its improvement is to identify the points where the flow is interrupted, sequences of activities and limited resources conditioning proactive capacity planning⁸. Different modeling tools have been developed to represent scenarios for decision making and to approach path-based management through a holistic perspective. Their selection will be in correspondence with basic aspects, such as multifaceted nature, uncertainty and flows complexity.

There are different methods to patient flow modeling: analytical approaches (queuing theory models, Markov chains and compartmental models), simulation-based approaches (discrete event simulation, agent-based simulation and system dynamics), and statistical or empirical approaches⁹. Their main objectives are capacity planning, resources allocation, resources and appointments scheduling, care processes change, and reducing patient delays.

Markov chains are stochastic processes with finite countable state space, where there is a loss of memory of past states, since only the position at the current instant is taken into account to know the probability of a change of state or not in the chain¹⁰. It takes into account parameters such as service time, waiting time, absorption state and phase type distribution. They have been applied to model the length of stay of patients in inpatient and surgical wards^11,12.

Those tools have evolved along time, accompanied by the level of hospital processes digitalization, supporting decision making. Their use for patient flows management is still focused on the occupancy of bed resource than on the trajectory. A previous bibliographic search revealed that there were no bibliometric studies showing the evolution of Markov chains application to improvement of patient flows in hospital institutions.

Consequently, the present research aims to evaluate the scientific activity related to the application of Markov chains in the improvement of patient flows in hospital institutions.