Queuing Model for Hospital Congestion with Application

Abstract

The emergence of Covid-19 posed a great health challenge worldwide. Health care facilities were stretched beyond limit, with no space to admit new critical patients. This motivated this study, which sought to understand the dynamics around queues, particularly in hospitals. The main objective was to analyze the queuing process between the Emergency Department (ED) and Internal Wards (IW) at Moi Teaching and Referral Hospital, in order to understand patient flow with the view to minimizing congestion. The study modelled the process as a queuing system with heterogeneous server pools, where the pools represent the wards and servers are beds. The system was analysed under various queue-architectures and routing policies, in search for fairness and optimum operational performance so as to enhance the level of access to health care in the facility. The existing models such as Kendall’s, Erlang’s, Little’s Law and De Bruin’s models were used to analyze various ward/unit operating characteristics and sufficient bed count was determined to guarantee certain access standards to care. The results indicated that there were long queues arising from blockage which led to higher chances of patients waiting for long hours for services in the facility. To solve the problem the study proposes reassignment of beds within the Hospital wards so that any arriving patient and those waiting for services are examined and allocated beds immediately. This will reduce the long waiting time for services and give the hospital sufficient time in daily operations.