Analysis of Coronavirus Patients Flow in Hospitals: An Application of Queuing Theory

During the Coronavirus disease 2019 crisis, many hospitals suffered from a severe shortage of resources. This was due to the exponential growth in the number of recorded cases. In many world countries, COVID-19 patients had to wait for a free bed which puts their lives at risk. Therefore, hospitals are forced to raise the limits of their permissible resources to be able to afford all cases. In this paper, The queuing theory model was used as an operations management technique to calculate the number of needed beds that must be available to cover all recorded cases. Based on the available information, Italy was chosen as a case study - which was one of the hotspot countries in the beginning of the crisis after China. An analysis of the behavior of the waiting lines in hospitals is introduced from the beginning of the crisis and for more than one year later. According to queuing theory formulas, the number of the required hospital beds and ICU beds are determined. Moreover, the probability of waiting and the utilization of the system are also calculated. By testing the system, we concluded that 20000 hospital beds were required to accommodate about 99% of hospital patients recorded in the highest period of infection. In addition, 2500 ICU beds were needed to serve 100% of ICU patients recorded in the same period. The expected waiting delay that patients suffered because of the waiting queues is also measured.