A Queuing Network Model with Blocking: Analysis of Congested Patient Flows in Mental Health Systems

The downsizing and closing of state mental health institutions in Philadelphia in the 1990’s led to the development of a continuum care network of residential-based services. Although the diversity of care settings increased, congestion in facilities caused many patients to unnecessarily spend extra days in intensive facilities. This study applies a queuing network system with blocking to analyze such congestion processes. “Blocking” denotes situations where patients are turned away from accommodations to which they are referred, and are thus forced to remain in their present facilities until space becomes available. Both mathematical and simulation results are presented and compared. Although queuing models have been used in numerous healthcare studies, the inclusion of blocking is still rare. We found that, in Philadelphia, the shortage of a particular type of facilities may have created “upstream blocking”. Thus removal of such facilityspecific bottlenecks may be the most efficient way to reduce congestion in the system as a whole.