A Queueing Model to Study Ambulance Offload Delays

The ambulance offload delay problem is a well-known result of overcrowding and congestion in emergency departments. Offload delay refers to the situation where area hospitals are unable to accept patients from regional ambulances in a timely manner due to lack of staff and bed capacity. The problem of offload delays is not a simple issue to resolve and has caused severe problems to the emergency medical services (EMS) providers, emergency department (ED) staff, and most importantly patients that are transferred to hospitals by ambulance. Except for several reports on the problem, not much research has been done on the subject. Almost all research to date has focused on either EMS or ED planning and operation and as far as we are aware there are no models which have considered the coordination of these units. We propose an analytical model which will allow us to analyze and explore the ambulance offload delay problem. We use queuing theory to construct a system representing the interaction of EMS and ED, and model the behavior of the system as a continuous time Markov chain. The matrix geometric method will be used to numerically compute various system performance measures under different conditions. We analyze the effect of adding more emergency beds in the ED, adding more ambulances, and reducing the ED patient length of stay, on various system performance measures such as the average number of ambulances in offload delay, average time in offload delay, and ambulance and bed utilization. We will show that adding more beds to the ED or reducing ED patient length of stay will have a positive impact on system performance and in particular will decrease the average number of ambulances experiencing offload delay and the average time in offload delay. Also, it will be shown that increasing the number of ambulances will have a negative impact on offload delays and increases the average number of ambulances in offload delay. However, other system performance measures are improved by adding more ambulances to the system. Finally, we will show the tradeoffs between adding more emergency beds, adding more ambulances, and reducing ED patient length of stay. We conclude that the hospital is the bottleneck in the system and in order to reduce ambulance offload delays, either hospital capacity has to be increased or ED patient length of stay is to be reduced