We use discrete event simulation to model and analyze a real-life emergency department (ED). Our approach relies on the appropriate integration of most real-life ED features to the simulation model in order to derive useful practical results. Data is supplied from the ED of the urban French hospital Saint Camille. Our purpose is to optimize the human resource staffing levels. We want to minimize the patient average length of stay (LOS), by integrating the staffing budget constraint and a constraint securing that the most severe incidents will see a doctor within a specified time limit. The second constraint allows to avoid the perverse effect of only considering the LOS metric that would delay the treatment of the most urgent patients. We use simulation-based optimization, in which we perform a sensitivity analysis expressing LOS as a function of the staffing budget and also the average door-to-doctor time for urgent patients (DTDT). We show that the budget has a diminishing marginal effect on the problem solution. Due to the correlation between LOS and DTDT, we also observe that the DTDT constraint may significantly affect the feasibility of the problem or the value of the optimal solution.