Analysis and optimization of an ambulance offload delay and allocation problem

Ambulance offload delays have recently become one of the most significant operational challenges for Emergency Medical Services (EMS) providers. Offload delays occur when an ambulance arriving at a hospital Emergency Department (ED) is blocked until a bed becomes available for the patient. To formally investigate the effect of patient routing decisions on EMS offload delays, we introduce a stylized queueing network model with blocking. Following a decomposition approach, we develop an approximation scheme to find explicit solutions that can be used to find proper patient allocation policies to multiple hospitals in a region. We introduce a Markov chain representation for a single ED network and solve for its exact steady state distribution. A comprehensive numerical study is carried out to validate the approximation approaches and to gain insight into ambulance offload delays. By keeping the total offload delays at minimal levels, we observe that it is better to load larger EDs more heavily than smaller ones due to resource pooling.