Modeling and optimization of a health care system

Abstract

In many applications, the number of elements in the system (i.e., machines, jobs, customers) is either constant or remain fixed. This type of a system is modeled as a closed queuing system. Closed queuing systems are those in which there is no exogenous arrival to the system and no element leaves the system. In these systems, departure from one state is an arrival to the next state. Those cases in which the system is always full and any departure from the system is immediately replaced by a new arrival are also considered closed systems. This closeness of the system changes the nature of the modeling process in which the well known queuing models need to be modified accordingly. In this research, a health care center with a limited number of beds which are used at their maximum capacity is considered. In this closed queuing system, available and reserved nurses are also modeled by means of closed queuing systems. Considering the interaction of the resulting networks, the optimal level of reserved nurses as well as the patients discharge and admission rates is determined in such a way that the incurred cost is minimized.