Hematopoiesis is a complex and strongly regulated process. In case of regenerative pressure, efficient recovery of blood cell counts is crucial for survival of an individual. We propose a quantitative mathematical model of white blood cell formation based on the following cell parameters: (1) proliferation rate, (2) self-renewal, and (3) cell death. Simulating this model we assess the change of these parameters under regenerative pressure. The proposed model allows to quantitatively describe the impact of these cell parameters on engraftment time after stem cell transplantation. Results indicate that enhanced self-renewal during the posttransplant period is crucial for efficient regeneration of blood cell counts while constant or reduced self-renewal leads to delayed recovery or graft failure. Increased cell death in the posttransplant period has a similar impact. In contrast, reduced proliferation or pre-homing cell death causes only mild delays in blood cell recovery which can be compensated sufficiently by increasing the dose of transplanted cells.