In this study we used a nonparametric statistical approach estimate time varying arrival rates to an Emergency Department (ED). These rates differ hourly within each month in a year. The time varying arrival rates serve as a key input into a new discrete-event simulation model for patient flow at an ED of the case study hospital. Our simulation model estimated Length of Stay (LOS) and Door to Doctor Time (DTDT) for patients in three different acuity groups. The simulation model also used for optimizing the staffing allocations in three different shifts. The methodological contributions are exemplified using real ED data from a major teaching hospital.