Motivated by the exceptionally high mortality statistics of dialysis patients and the ongoing debate about the adequacy of the current reimbursement for the dialysis in the United States, we pursue a detailed analysis of the dialysis delivery system. The analysis is based on a multiclass fluid model for the dialysis facility, which combines a pharmacokinetics model of dialysis and an empirically validated model of dialysis-specific mortality. Assuming that the facility operates under the budget and capacity constraints, our analysis determines the main factors that affect the delivery of dialysis. Numerical results, which are representative of the dialysis environment in the US, demonstrate the accuracy of the model and provide concrete insights about the operations of the dialysis facility. A major finding is that an improvement in the technology of dialysis is likely to have a more substantial impact on the overall life expectancy of the dialysis population as compared to an increase in the dialysis reimbursement rate.