In this work, we produce several prediction models for aspects of hospital emergency departments. Firstly, we demonstrate the use of a recurrent neural network to predict the rate of patient arrival at a hospital emergency department. The prediction is made on a per hour basis using date, time, calendar, and weather information. Then, we present our comparison of two prediction systems on the task of replicating the human decisions of patient admittance in a typical American emergency department. Again, a recurrent neural network (RNN) was trained to learn the task of selecting the next patient from the waiting room/queue to be admitted for treatment. Lastly, we present our attempt to produce a regression model that can predict the likelihood that a given patient will leave after waiting a specific amount of time in the emergency department’s waiting-room/queue. Such a model could be used to optimize the patient’s waiting-room/queue of an ED to minimize the likelihood of patients leaving without receiving care.